Variable ratio reaction valve

ABSTRACT

A reaction type control valve, primarily intended for controlling a power assisted steering system, comprising a hydraulic interface having variable effective reaction areas, the extent of which is determined by selected functions of values of torque applied thereto. Differential hydraulic fluid pressure is generated by the valve, which differential hydraulic fluid pressure is proportional to the applied torque and inversely proportional to any particular effective reaction area. Hydraulic fluid is induced to flow through a hydraulic interface between first and second valve members wherein primary and secondary sets of input and return orifices are selectively utilized to define the effective reaction areas as a function of the input torque. The primary and secondary sets of input and return orifices are located at selected radii. The selected radii locating the primary sets of input and return orifices comprise first and second radii, respectively, wherein the first radii are smaller in value than the second radii. The selected radii locating the secondary sets of input and return orifices comprises third and fourth radii, respectively, wherein the third radii are smaller in value than the fourth radii. And, the difference between the second radii and the first radii is greater than the difference between the fourth radii and the third radii.

CROSS-REFERENCE TO RELATED APPLICATION

This is a continuation-in-part application of U.S. patent applicationSer. No. 461,541 filed on Jan. 5, 1990 (now abandoned).

TECHNICAL FIELD

This invention relates generally to hydraulically controlled powersteering systems and particularly to such systems which utilize four-wayopen-center hydraulic reaction control valves.

BACKGROUND OF THE INVENTION

Four-way open-center control valves (hereinafter "four-way valves")which use constant flow rate hydraulic power sources are commonlyutilized for controlling vehicular power steering systems. Such systemstypically employ a four-way rotary valve having "follow along" positionfeedback. Road feel is artificially induced by deflection of a torsionbar.

An earlier type of power steering system provided feedback partiallyproportional to actual steering effort. This power steering systemfeatured a four-way open-center hydraulic reaction control valve(hereinafter "reaction valve"). However, such systems were relativelyexpensive to manufacture and were generally replaced in this country byrotary valve equipped power steering systems. (Note, however, reactionvalve equipped power steering systems are still commonly manufacturedoverseas.)

A rotary valve is a four-way open-center flow control valve which hascircumferentially close fitting inner and outer valve members. The innerand outer valve members usually feature four sets each of pressure,first and second output, and return slots. These four sets of slots areequally spaced (at 90 degrees) around the interfacing circumferences ofthe inner and outer valve members. Differentially controlled outputflows in the first and second output slots are obtained by rotationallydisplacing the inner valve member with respect to outer valve member.

The open-center configuration of the rotary valve allows a nominallyconstant flow hydraulic fluid source to be utilized. In normaloperation, at other than small valve displacements, system supplypressure nominally approximates differential output pressure(hereinafter "output pressure"). This results in minimum system powerconsumption but results in wildly erratic system control characteristicswherein assist levels can vary by more than 40:1.

In preferred embodiments of the invention, hydraulic reaction torque isgenerated between inner and outer valve members which are formed withmultiple control orifices having differing radii. The control orificescomprise input control orifices which meter fluid from a constant flowhydraulic fluid source into an output port and return control orificeswhich meter fluid returned therefrom to a tank.

The input control orifices are formed at smaller radii than the returncontrol orifices. Thus, output pressure between the first and secondoutput ports is additively applied to either side of each of a pluralityof effectively enlarged ridge sections which form the return controlorifices. The product of the output pressure, the summed areas of theenlarged ridge sections, and their effective radii generates thehydraulic reaction torque.

Output pressure is coupled to a utilization device, such as a powercylinder, via flow restrictors. The flow restrictors are controlledorifice devices which have a nominally linear flow resistancecharacteristic. For this reason, values of differential pressure appliedto the utilization device are different than the output pressure. Thechange in output pressure is nominally proportional to fluid flow ratethrough the utilization device. This results in a controlled dampingratio and stable operation of systems incorporating the flow restrictorsof the present invention.

Improved performance can be obtained from a servo system comprising atorque reaction valve by introducing an orifice in parallel with autilization device also comprised within the servo system. Fluid flowrate through the orifice improves system damping and results in animproved control characteristic wherein over-sensitive response to smallinvoluntary control inputs is precluded.

In a first set of preferred embodiments, U.S. patent application Ser.No. 461,541 discloses four-way torque reaction valves which comprise anouter valve member directly coupled to an input shaft. The outer valvemember comprises various hydraulic slip rings which are subject tosubstantial hydraulic pressures and are sealed via four seal rings in aknown manner. However, because the outer valve member is directlycoupled to the input shaft, the seal rings can provide excessivetangential drag on the input shaft when system pressures are high. Thus,in accordance with a second set of preferred embodiments of thatinvention, torque reaction valves comprising tangentiallynon-constrained input shafts are also described. This is accomplishedvia mechanically coupling the input shaft to a torsionally compliantspring member utilized for applying torque to a tangentially floatinginner valve member.

A power steering system utilizing either of the torque reaction valvesdescribed above exhibits a substantially linear characteristic whereinsteering wheel torque is proportional to steering load. However, someprefer a non-linear torque reaction valve wherein moderately increasingvalues of hydraulic gain are provided concomitantly with increasingsteering loads. This enables increased tactile feel of lighter steeringloads concomitant with relatively decreased values of steering wheeltorque at higher steering loads.

It has been found that a torque reaction valve having an even strongernon-linear characteristic is desired. Furthermore, the predominantnon-linearities of such a valve should be present at highest steeringloads. Because input torque is linearly dependent upon the summedeffective differential area (hereinafter "effective area") of the torquereaction valve, as described above, this new requirement can mosteffectively be met via reducing the effective area as a function ofoutput pressure.

SUMMARY OF THE INVENTION

In preferred embodiments of the present invention, improved torquereaction valves are disclosed wherein effective reaction area varies asa function of input torque. As input torque is increased, effectivereaction area decreases as a function of valve motion and thereforeoutput pressure. Thus, the ratio between output pressure and inputtorque concomitantly increases whereby the improved torque reactionvalves may be described as variable ratio reaction valves.

In the variable ratio reaction valves, a torsion bar is utilized as thecompliant spring member mentioned above. The torsion bar is utilized tocouple torque from an input shaft to a tangentially floating inner valvemember. A torsion bar extension additionally couples a portion of theinput torque directly to a pinion shaft member of an outputrack-and-pinion set of a host power steering system. An outer valvemember is directly coupled to the pinion shaft. An effective hydraulicinterface area disposed between the inner and outer valve memberstransmits the remaining portion of the input torque to the outer valvemember from whence it is directly applied to the pinion shaft as well.

Output pressure proportional to the ratio of the remaining portion ofthe applied torque divided by the effective area is generated by thevariable ratio reaction valves. The output pressure is delivered to adouble-acting cylinder of the host power steering system. The product ofthe output pressure and the piston area of the double-acting cylindercomprises steering assist force which supplements mechanical steeringforce directly generated via a rack member of the output rack-and-pinionset.

The effective area varies as a function of applied torque via thefollowing method: Secondary sets of control orifices, which arehydraulically in series with the primary sets of control orificesdescribed above, supplement the pressure controlling process within thevariable ratio reaction valves. The secondary sets of control orificesare formed at radii much closer in value than the primary sets ofcontrol radii. In addition, each of the primary sets of control orificesare formed with radial clearance between their inner and outer controledges whereby pressure control smoothly inverts from a nominally equallyshared pressure control to dominant pressure control by the secondarysets of control orifices. In a modified variable ratio reaction valve,the primary sets of control orifices are partially defined by a slopingsurface whereby dominant pressure control smoothly inverts from theprimary sets of control orifices to the secondary sets of controlorifices.

In each case, as applied torque values increase, the net closure rate ofthe secondary set of control orifices becomes greater than that of theprimary set of control orifices. Thus, the secondary set of controlorifices progressively become dominant in determining pressure dropswithin the variable ratio reaction valve. Since the interface areadetermined by the secondary set of control orifices is smaller than thatof the primary set of control orifices, the rate of change, or gain, ofoutput pressure to the input torque is greater at higher values of inputtorque.

Two practical mechanical design aspects of the variable ratio reactionvalves are also addressed herein. Firstly, a radial over-constraintresulting from utilizing a single torsion bar for both the previouslydescribed torsion bar and torsion bar extension functions is discussed.The over-constraint results from the torsion bar being attached at threepoints; the input shaft, the inner valve member and the pinion shaft.This over-constraint is ameliorated by making all attachments viaco-planer pins. In the pin axes plane, infinite compliance is obtainedat the center attachment point because that pin is a slip fit in a holein the torsion bar. And, by preferred placement of reduced diametersportions of the torsion bar, radial compliance of center attachmentpoint in the orthogonal direction, about the pinned ends of the torsionbar, is maximized.

Secondly, the inner valve member is subject to widely varying pressuresbetween the various slots and control orifices on its outer peripheryand its inside diameter. Thus, leakage flow occurs across its endsurfaces. Pressure distributions thereon depend upon the fine geometryof the surfaces of the inner valve member and members on either end ofthe inner valve member which define the leakage flow channels.Asymmetrical pressure distributions resulting therefrom could cockand/or drive the inner valve member against one, or both, of the memberson either end. This could result in excessive friction which couldresult in the inner valve member being held securely against the memberson either end--a condition commonly referred to as "hydraulic lock".

Lateral force induced hydraulic lock in spool valves is a seriousproblem because it is normally not feasible to form hydrostatic bearingsurfaces which support the spool member of such spool valves. Thus,multiple circumferential grooves are often formed on lands of the spoolmembers. Then fluid merely flows around the lands and limits lateralpressure build-up.

However, in the case of the variable ratio reaction valves, it ispossible to eliminate the problem at its source. This can beaccomplished by lapping each end of the inner valve member so as to forma slightly convex surface thereon. The resulting converging leakage flowchannels effectively form hydrostatic bearings which fluidically centerthe inner valve member between the members on either end.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diametrical section view of a torque reaction valveaccording to a preferred embodiment of the present invention.

FIG. 2A is a diametrical section view of a torque reaction valveaccording to an alternate preferred embodiment of the present invention.

FIGS. 2B and 2C are enlarged sectional views of an inlet control orificeand a return control orifice, respectively, of the torque reaction valveof FIG. 2A.

FIG. 3 is a longitudinal section view of a four-way torque reactionvalve which is representative of the torque reaction valves of bothFIGS. 1 and 2A-C.

FIG. 4 is a longitudinal section view of a hand operated controllerwhich comprises a four-way torque reaction valve.

FIG. 5A is a longitudinal section view of an electro-hydraulic servovalve which comprises a four-way torque reaction valve.

FIG. 5B is an end view which illustrates a preferred embodiment of alimited excursion torque motor utilized with the electro-hydraulic servovalve shown in FIG. 5A.

FIG. 6 is a sectional view of two directional controlled orifice flowrestrictors (herein called "hydraulic resistors") which are mountedside-by-side and oriented in opposite directions.

FIG. 7 is a sectional view of a single controlled orifice flowrestrictor mounted within a check valve.

FIG. 8 is a graph showing flow resistance, pressure drop and flow ratevs. displacement for a controlled orifice flow restrictor.

FIG. 9 is a graph showing contoured valve member clearance vs.displacement for a controlled orifice flow restrictor.

FIG. 10A, 10B and 10C are diagrammatic graphs which illustrate positionsof a controlled orifice for displacements corresponding to zero, quarterand full-flow, respectively.

FIG. 11 is a schematic drawing of a simple open-loop control systemwherein a four-way torque reaction valve and a hydraulic resistor areutilized to control the position of a mass via a double acting hydrauliccylinder.

FIGS. 12A and 12B are Bode diagrams which illustrate the dynamicperformance range of the open-loop control system of FIG. 11.

FIG. 13 is a block diagram which depicts a closed-loop servo systemcomprising the open-loop control system illustrated in FIG. 11.

FIG. 14 is a sectional view of an orifice which is hydraulically inparallel with a piston of the double acting cylinder and which is usedto improve the dynamic characteristics of the open-loop control systemof FIG. 11.

FIG. 15 is a schematic drawing of an enhanced open-loop control systemwhich additionally comprises the orifice shown in FIG. 10 and blockrepresenting a load placed upon the piston of the double actingcylinder.

FIG. 16 is a graph illustrating output force/torque vs. torque for theopen-loop control system of FIG. 15.

FIGS. 17A and 17B are Bode diagrams which illustrate the dynamicperformance range of the open-loop control system of FIG. 15 for outputforces of 10 (lbs), 100 (lbs), and 1000 (lbs).

FIGS. 18A and 18B are Bode diagrams which illustrate the dynamicperformance range of the open-loop control system of FIG. 15 forvelocities of 0 (in./sec.), 1 (in./sec.), and 4 (in./sec.) and an outputforce of 1000 (lbs).

FIG. 19 is a flow chart outlining a method of controlling a closed-loopservo system comprising a four-way torque reaction valve.

FIG. 20 is a flow chart outlining a method of controlling an open-loopservo system comprising a hand operated controller.

FIG. 21 is a flow chart outlining a method of controlling a closed oropen-loop servo system comprising an electro-hydraulic servo valve.

FIG. 22A is a longitudinal section view of a hand operated controllerwhich comprises an improved torque reaction valve.

FIG. 22B is a transverse section view of the hand operated controller ofFIG. 22A depicting placement of damper and check valves used therein.

FIGS. 23A and 23B are isometric views of inner and outer valve membersused in the hand operated controller of FIG. 22A.

FIGS. 24A and 24B are sectional views of the damper and check valvesused in the hand operated controller of FIG. 22A.

FIGS. 25A and 25B are isometric views of alternate barrier rings used inthe hand operated controller of FIG. 22A to configure it as a four orthree-way valve, respectively.

FIG. 26 is an isometric view of a torsion bar used in the hand operatedcontroller of FIG. 22A.

FIG. 27 is a longitudinal section view of an electro-hydraulic servovalve which comprises the improved torque reaction valve.

FIG. 28 is a section view of a first torque reaction valve whichcomprises follow along position feedback.

FIG. 29 is a section view of a second torque reaction valve which alsocomprises follow along position feedback.

FIG. 30A is a block diagram which depicts the operation of a powersteering system that utilizes either of the first or second torquereaction valves.

FIG. 30B is a block diagram which depicts the operation of an outputsection of the block diagram shown in FIG. 30A.

FIG. 31 is a "cononical form" of feedback control system to which theblock diagram of FIG. 30A can be reduced via computation of forward andfeedback transfer functions.

FIGS. 32A-C are plots depicting steering force as a function of appliedtorque, tangential valve motion and input shaft rotation, respectively,for the first torque reaction valve.

FIGS. 33A-C are plots depicting steering force as a function of appliedtorque, tangential valve motion and input shaft rotation, respectively,for the second torque reaction valve.

FIGS. 34A-H are plots depicting performance of a power steeling systemutilizing the first torque reaction valve for a low value of steeringforce.

FIGS. 35A-H are plots depicting performance of a power steeling systemutilizing the first torque reaction valve for a high value of steeringforce.

FIGS. 36A-H are plots depicting performance of a power steering systemutilizing the second torque reaction valve for a low value of steeringforce.

FIGS. 37A-H are plots depicting performance of a power steering systemutilizing the second torque reaction valve for a high value of steeringforce.

FIG. 38 is a section view of a variable ratio reaction valve whichcomprises follow along position feedback.

FIG. 39 is an enlarged section view of a segment of inner and outervalve members of the variable ratio reaction valve of FIG. 38 whereinthe inner valve member is located in a centered position concomitantwith a zero value of input torque.

FIGS. 40A and 40B are similarly enlarged section views of portions ofthe inner and outer valve members depicted in relative positionsconcomitant with high values of counterclockwise and clockwise inputtorques, respectively.

FIGS. 41A and 41B are descriptive section views depicting positions ofprimary and secondary return control orifices of a variable ratioreaction valve concomitant with a zero value and a large value of inputtorque, respectively.

FIG. 42 is an enlarged end view of the inner valve member of thevariable ratio reaction valve.

FIG. 43 is an enlarged and view of the outer valve member of thevariable ratio reaction valve.

FIGS. 44A and 44B are descriptive side views of assemblies comprisingthe inner valve member which illustrate supporting hydrostatic bearingsformed by convex lapped surfaces formed thereon and stepped surfacesformed on juxtaposed surfaces, respectively.

FIG. 45 is a side view of a drive pin used to transmit input torque tothe inner valve member which illustrates a crowned tooth profile usedthereon.

FIGS. 46A-C are plots depicting steering force as a function of appliedtorque, tangential valve motion and input shaft rotation, respectively,for a variable ratio reaction valve.

FIGS. 47A-H are plots depicting performance of a power steering systemutilizing the variable ratio reaction valve for a high value of steeringforce.

FIGS. 48A-B are descriptive section views depicting positions of primaryand secondary input control orifices of a modified variable ratioreaction valve concomitant with a zero value and a large value of inputtorque, respectively.

FIGS. 49A-B are descriptive section views depicting positions of primaryand secondary return control orifices of a variable ratio reaction valveconcomitant with a zero value and a large value of input torque,respectively.

FIG. 50 is an enlarged end view of a modified inner valve member of amodified variable ratio reaction valve.

FIG. 51 is an enlarged end view of a modified outer valve member of themodified variable ratio reaction valve.

FIGS. 52A-C are plots depicting steering force as a function of appliedtorque, tangential valve motion and input shaft rotation, respectively,for the modified variable ratio reaction valve.

FIGS. 53A-H are plots depicting performance of a power steering systemutilizing the modified variable ratio reaction valve for a high value ofsteering force.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention embodies apparatus and control methods whichenable proportional and stable control of the position of ahydraulically actuated, double acting utilization device. In the presentinvention, a four-way torque reaction valve is provided wherein reactiontorque is generated within the four-way torque reaction valve itself.This is accomplished by applying output pressure directly betweendifferential surfaces of first and second valve members. Torqueapplication therebetween is unopposed by any spring member analogous tothose commonly found on known types of reaction valves. One example isthat of a so-called "star" valve as described in U.S. Pat. No. 4,217,932by Juan S. Bacardit which is entitled HYDRAULIC ROTARY DISTRIBUTER,PARTICULARLY FOR USE IN POWER STEERING SYSTEMS and was issued on Aug.19, 1980.

Closed-loop servo systems utilizing the four-way torque reaction valveof the present invention to position a mass are stabilized by energyloss associated with motion of the mass. In order to positively controlthe magnitude of such energy loss, a damper valve assembly, also of thepresent invention, may be introduced into hydraulic circuits comprisedwithin such closed-loop servo systems.

Shown in FIG. 1 is a diametrical section view of a four-way torquereaction valve 210. The four-way torque reaction valve 210 comprises atorsion bar 213, inner and outer valve members 212 and 214,respectively, and a valve body 215. As will be described below, inputtorque is applied to the outer valve member 214 while feedback torque isapplied to the inner valve member 212 via the torsion bar 213. Then themagnitude of the resulting output pressure is linearly related to theapplied torque.

Fluid from the constant flow hydraulic fluid source (not shown) flowsinto the four-way torque reaction valve 210 via input ports 216 and intopressure slots 218. The fluid then flows past either or both sets offirst and second input control orifices 220 and 222, respectively, tosets of first and second output slots 224 and 226, respectively. Aselected portion of the fluid flows out one of first and second outputports 228 and 230, respectively, to a double acting utilization device(not shown) and returns therefrom via the other one of the first andsecond output ports 228 and 230, respectively. The fluid then flows pasteither or both sets of first and second return control orifices 232 and234, respectively, into return slots 236 The fluid is then returned to atank (not shown) via return ports 238 and an internal drain path (alsonot shown).

All of the above described ports, slots and control orifices aredepicted as balanced sets of two ports, slots and control orifices,respectively. Such balanced pairs of ports, slots and control orificeseliminate radial forces between the inner and outer valve members 212and 214, respectively. In general, any number, N, of ports, slots andcontrol orifices greater than one (arranged, however, in a balancedmanner) may be utilized for the various sets of ports, slots and controlorifices. Sets of four (i.e., N=4) ports, slots and control orifices areparticularly common.

Outside surfaces 240 of the inner valve member 212 and inside surfaces242 of the outer valve member 214 comprise functional surfaces of thefirst and second sets of input control orifices 220 and 222,respectively, and are radially sized with minimal clearancetherebetween. Lands 244 of the inner valve member 212 are formedselectively narrower than the pressure slots 218 of the outer valvemember 214 in order to effect proper underlapped valve input orifice(i.e., open center) characteristics. Similarly, outside surfaces 246 ofthe inner valve member 212 and inside surfaces 248 of the outer valvemember 214 comprise functional surfaces of the first and second sets ofreturn control orifices 232 and 234, respectively, and are sized withminimal clearance therebetween. Lands 250 of the inner valve member 212are formed selectively narrower than the return slots 236 of the outervalve member 214 in order to effect underlapped valve return orificecharacteristics.

Output pressure comprises the difference between first and second valuesof pressure present in the first and second output slots 224 and 226,respectively. The first and second values of pressure communicate withboth lateral surfaces 252 and 254, and lateral surfaces 256 and 258,respectively. In addition, the outside surfaces 246 of the inner valvemember are formed at larger radii than the outside surfaces 240 of theinner valve member. Thus, the lateral surfaces 254 and 258 are larger inarea and are located at larger effective radii than the lateral surfaces252 and 256, respectively. Therefore, non-zero output pressures willconcomitantly generate torque between the inner valve member 212 and theouter valve member 214. The torque generated therebetween is determinedby

    T=A.sub.v PR.sub.v

where T is the torque, A_(v) is effective net valve area (and is equalto the product of the difference in radii between the outside surfaces246 and the outside surfaces 240, length of the valve, and N), P is theoutput pressure and R_(v) is the effective radius of the effective netvalve area, A_(v).

Shown in FIG. 2A is a diametrical section view of an another preferredembodiment of a four-way torque reaction valve 260 also of the presentinvention. The four-way torque reaction valve 260 comprises inner andouter valve members 262 and 264, respectively. Fluid from a constantflow hydraulic fluid source (not shown) flows into the four-way torquereaction valve 260 via input ports 266 and into pressure slots 268. Thefluid then flows past either or both sets of first and second inputcontrol orifices 270 and 272, respectively, to sets of first and secondoutput slots 274 and 276, respectively. A selected portion of the fluidflows out one of first and second output ports 278 and 280,respectively, to a double acting utilization device (not shown) andreturns therefrom via the other one of the first and second output ports278 and 280, respectively. The fluid then flows past either or both setsof first and second return control orifices 282 and 284, respectively,into return slots 286. The fluid is then returned to a tank (not shown)via return ports 288 and an internal drain path (also not shown).

All of the above described ports, slots and control orifices aredepicted as balanced sets of two ports, slots and control orifices,respectively. Such balanced pairs of ports, slots and control orificeseliminate radial forces between the inner and outer valve members 262and 264, respectively. In general, any number of ports, slots andcontrol orifices greater than one (arranged, however, in a balancedmanner) may be utilized for the various sets of ports, slots and controlorifices. Sets of four ports, slots and control orifices areparticularly common.

Outside surfaces 290 of the inner valve member 262 are formed at alarger radius than inside surfaces 292 of the outer valve member 264.This is shown more clearly in FIG. 2B which is an enlarged sectionalview of one set of a pressure slot 268 and first and second inputcontrol orifices 270 and 272, respectively. The first and second inputcontrol orifices 270 and 272, respectively, comprise lateral surfaces294 and 296 of a land 298 of the inner valve member 262 and lateralsurfaces 300 and 302 of the pressure slot 268, respectively. The lateralsurfaces 294 and 296, and the lateral surfaces 300 and 302, are formedsuch that gaps 304 and 306 therebetween become progressively narrowerwith respect to fluid flow direction which occurs from larger to smallerradii therebetween. Thus, the first and second input control orifices270 and 272, respectively, are formed in the manner of reducing nozzleswhose exit widths are the minimum values of the gaps 304 and 306,respectively.

Outside surfaces 310 of the inner valve member 262 are formed at alarger radius than inside surfaces 312 of the outer valve member 264.This is shown more clearly in FIG. 2C which is an enlarged sectionalview of one set of a return slot 286 and first and second return controlorifices 282 and 284, respectively. The first and second return controlorifices 282 and 284, respectively, comprise lateral surfaces 314 and316 of a land 318 of the inner valve member 262 and lateral surfaces 320and 322 of the return slot 286, respectively. The lateral surfaces 314and 316, and the lateral surfaces 320 and 322, are formed such that gaps324 and 326 therebetween become progressively narrower with respect tofluid flow direction which occurs from smaller to larger radiitherebetween. Thus, the first and second return control orifices 282 and284, respectively, are formed in the manner of reducing nozzles whoseexit widths are the minimum valves of the gaps 324 and 326,respectively. Ideally, the exit widths of the gaps 304, 306, 324 and 326are all made substantially equal.

Although the lateral surfaces 314 and 316 are depicted as being formedparallel to one another, they may be formed in a manner identical to thelateral surfaces 294 and 296. If this is done, the toothlikeconfiguration of the inner valve member 263 may be formed onconventional spur gear fabricating equipment. Then the lateral surfaces320 and 322 are formed at a larger angle, thus maintaining the reducingnozzle configurations of the return control orifices 282 and 284.

The output pressure comprises the difference between first and secondvalues of pressure present in the first and second output slots 274 and276, respectively. The first and second values of pressure communicatewith both lateral surfaces 294 and 314, and lateral surfaces 296 and316, respectively. Even though the outside surfaces 290 and 31 0 of theinner valve member 262 may be formed at equal radii (as shown in FIG.2A), the effective radial positions of the first and second returncontrol orifices 282 and 284, respectively, are formed at larger radiithan the effective radial positions of the first and second inputcontrol orifices 270 and 272, respectively. This is because theeffective radial position of the first and second input control orifices270 and 272, respectively, are formed at substantially the same radiusas the inner surfaces 292 of the outer valve member 264.

Thus, portions of the lateral surfaces 314 and 316 which are subjectedto the output pressure are larger in area and are located at largereffective radii than portions of the lateral surfaces 294 and 296 whichare subjected to the output pressure, respectively. Therefore, non-zerooutput pressures will concomitantly generate torque between the innervalve member 262 and the outer valve member 264. The torque generatedtherebetween is determined by

    T=A.sub.v PR.sub.v

(where in this case A_(v) is equal to the product of the difference inradii of the portions of the lateral surfaces 314 and 316, and 294 and296, respectively, which are subjected to the output pressure, thelength of the valve, and N).

Shown in FIG. 3 is a longitudinal section view which is representativeof either the four-way torque reaction valve 210 or the four-way torquereaction valve 260. (The description that follows uses the part numbersshown in FIG. 1 for the four-way torque reaction valve 210. However, thefollowing description applies equally to the four-way torque reactionvalve 260 and could be repeated using the part numbers shown in FIGS.2A-C. Therefore, it should be considered to be a generic discussionequally applicable to both the four-way torque reaction valves 210 and260.)

Disposed within the lower end of the valve body 215 is a pinion shaft328. It is located therein by ball bearings 330 and 332 wherein axialpreload is provided by Belleville spring washers 334 and retaining nut336. Mounted adjacent the ball bearing 330 is another ball bearing 338upon whose outer race is located the lower end of the outer valve member214 via a counterbore 340 therein.

Pinion gear teeth 342 are formed on the pinion shaft 328. Rack gearteeth 344 of a rack assembly 346 are held in mesh with the pinion gearteeth 342 by a spring loaded bearing yoke 348 in a known manner. Axiallydisposed along the rack assembly 346 is a piston 350. The piston 350 islocated within a double acting cylinder 352 formed within a casting 354which also comprises the valve body 215--all formed in a known manner. Ashaft seal 356 provides a barrier to migration of either hypoid oilcommonly utilized to lubricate the rack-and-pinion gear section or powersteering fluid commonly utilized as fluid within the four-way torquereaction valve 210.

Fixedly mounted within a bore 358 formed within the pinion shaft 328 isthe lower end of the torsion bar 213. The torsion bar 213 is retainedand rotationally oriented therein by a pin 360. The upper end of thetorsion bar 213 is formed with a male spline 362. To facilitate laterassembly of the inner valve member 212 thereon, the male spline 362 isformed with a number of teeth equal to an integral multiple of thenumber N of sets of ports, slots and control orifices comprised in theinner and outer valve members 212 and 214, respectively, wherein theteeth are rotationally oriented in a selective manner with respect tothe pin 360.

The outer valve member 214 is formed with a counterbore 366 in its lowerend and a counterbore 368 in its upper end. The inner valve member 212is axially assembled within the outer valve member 214. Barrier rings370 are assembled within the counterbores 366 and 368 and forciblyretained at the ends thereof by beveled internal retaining rings such asWaldes Truarc part number N5002-112 manufactured by Waldes Kohinoor,Inc. of Long Island City, N.Y.

The axial region 372 (of the axially assembled inner and outer valvemembers 212 and 214, respectively) comprises the active portions of thefour-way torque reaction valve 210 as shown in FIG. 1 (or 260 as shownin FIGS. 2A-C). The respective lengths of the active portions of theinner and outer valve members 212 and 214 are formed such that there isminimal axial operating clearance between the inner valve member 212 andthe barder rings 370. The minimal operating clearance provides a nominalflow barrier between the various slots and control orifices.Concomitantly, bores 374 of the barrier rings 370 and shaft portions 376of the inner valve member 212 are formed such that a free runningbearing fit is established therebetween.

A splined hole 378 is formed in the upper end of the inner valve member212. The splined hole 378 is sized such that it achieves a slideablemesh with the male spline 362. In addition, it is rotationally orientedsuch that a selected orientation of the inner valve member with respectto the male spline and therefore the pin 360 can be maintained. Thus,feedback torque is transmitted substantially without hysteresis from thepinion shaft 328 to the inner valve member 212 via the pin 360, angulardeflection of the torsion bar 213, and mesh of the male spline 362 andthe splined hole 378. This method of a transmitting the feedback torqueavoids axial overconstraint between the inner valve member 212 andeither of the barrier rings 370.

An input shaft 380 is located with respect to counterbore 382 and face384 of the outer valve member 214 by a pilot boss 386 and a shoulder388. It is affixed thereto alternately by a plurality of pins 390 or aplurality of set-screws 392 wherein the set-screws 392 are threadablyengaged in threaded half holes 394 in the outer valve member 214 andbear against the bottom of half holes 396 in the input shaft 380. Theadvantage of affixing the input shaft 380 to the outer valve member 214via the plurality of set-screws 392 is that subsequent disassembly ofthe torque reaction valve 210 is thereby facilitated.

A ball bearing 398 and a shaft seal 400 are installed in an inputhousing 402. A wave washer 399, the ball bearing 398 and shaft seal 400are slideably assembled over the input shaft 380 as the input housing402 is axially installed onto the valve body 215. The input housing 402is located radially in main bore 404 of the valve body 215 by a pilotboss 406 and affixed to the valve body 215 by treaded bolts (not shown).Hydraulic fluid is prevented from leaking between the input housing 402and the valve body 215 by an O-ring seal 408.

Fluid flows through the four-way torque reaction valve 210 generally asdescribed above with respect to FIG. 1. However, detailed fluid flowinto and/or out of the rotating assembly of the inner and outer valvemembers 212 and 214, respectively, is as follows:

Input fluid flows from a fluid source (not shown) through an input line410, input fitting 411 and input passage 412 through an input slip ring414 and finally to each of the input ports 216. Similarly, output fluidflows to or from either of the sets of first and second output ports 228and 230, respectively, via first or second output slip rings 416 and418, respectively, through first or second output passages 420 and 422,respectively, first or second output fittings 424 and 425, respectively,and first and second output lines 426 and 427, respectively, to or fromeither end of the cylinder 352, respectively. Finally, return fluid fromthe return ports 238 flows into an annular cavity 428 occupying thespace between the torsion bar 213 and the inside of the inner valvemember 212, out through return holes 429 and 430, and through returnslip ring 432, return passage 434, return fitting 436 and return line437 to a tank (not shown). In addition, four seal rings 439 are utilizedto preclude leakage from the input slip ring 414 or either of the outputslip rings 416 and 418.

In operation, a torque T(in.lbs) is applied to splines 438 formed on theinput shaft 380. The torque is transmitted to the outer valve member 214via the pins 390 or set-screws 392 and the outer valve member 214rotates slightly. One of the sets of first and second input controlorifices 220 and 222, respectively, and the other of the sets of returncontrol orifices 232 or 234, respectively, is enlarged in area while theopposite sets are reduced in area. Output pressure is generated whichmay result in motion of the piston 350 via fluid flow to and from thecylinder 352. Any motion of the piston 350 will concomitantly result inmotion of the rack assembly 346 and "follow up" rotational motion of thepinion 328 and lower end of the torsion bar 213. This rotational motionof the lower end of the torsion bar 213 will generally lag the rotationof the outer valve member 214 by a slight angle which may be thought ofas servo system error.

Concomitantly, the applied torque will be opposed by an identical torquegenerated by the output pressure acting upon the effective net valvearea as defined above (i.e., wherein T=A_(v) PR_(v)). This torque willalso cause the inner valve member 212 to rotate in the same direction asthe outer valve member 214 (but with less error than the pinion shaft328) and impart concomitant rotation to the upper end of the torsion bar213 via the splined hole 378 and the male spline 362. The simultaneouslagging rotation of the lower end and almost full rotation of the upperend of the torsion bar 213 results in the torsion bar 213 twisting by anangle θ.sub.θ (rad.). The angle θ.sub.θ is a measurement error anglewith the value.

    θ.sub.θ =10.2(1.sub.t Gd.sub.t.sup.4)

where 1_(t) is the effective length of the torsion bar 213, G is theshearing modulus of elasticity, and d_(t) is the diameter of theeffective length of the torsion bar 213. Thus, the relative angulardisplacement of the inner valve member 212 with respect to the pinionshaft 328 is linearly related to the applied torque T and has the valueθ.sub.θ --which can be evaluated as defined above.

Should a failure of the hydraulic system occur (i.e., such as by failureof a pump supplying fluid to the four-way torque reaction valve 210),the feedback torque will be absent and θ.sub.θ must be otherwiselimited. This is accomplished in the four-way torque reaction valve 210by a tangentially loose fitting spline set 440 comprising a male spline442 formed on the upper end of the pinion shaft 328 and a female spline444 formed within the outer valve member 214. Thus, such a failure wouldresult in the applied torque T being directly applied to the pinionshaft 328 via the spline set 440.

To facilitate axial assembly of the preassembled inner and outer valvemembers 212 and 214, respectively, onto the ball bearing 338 and themale spline 362 of the torsion bar 213, the spline set 440 is formedwith a number of teeth equal to an integral multiple of the number N ofsets of ports, slots and control orifices comprised within thepreassembled inner and outer valve members 212 and 214, respectively.

Although application to vehicular power steering has been assumedhereinabove in discussion of the four-way torque reaction valve 210, nosuch limitation in its use is appropriate. The four-way torque reactionvalve 210 can be used together with any hydraulically actuated, doubleacting utilization device to perform a wide variety of tasks. All thatis required to complete closed-loop systems utilizing the tour-waytorque reaction valve 210 is a suitable feedback path enablingapplication of feedback torque to the bottom end of the torsion bar 213.

Rotational motions greater than the angle θ.sub.θ are not necessarilyrequired in such systems. For instance, the four-way torque reactionvalve 210 could be used in a very simple servo system to position acylinder driven slide against a travel limit. All that would be requiredwould be a spring bias on the rack assembly 346 which urges the cylinderdriven slide toward the travel limit. When the travel limit struck theend of the rack assembly 346, the servo system would control thecylinder driven slide's position against the travel limit. Thepossibilities are endless and no attempt is made to catalog them byincluding a large number of additional application oriented figuresherein.

In addition, it is possible to use the basic apparatus of the torquereaction valve as an independent controller without feedback. Forinstance, shown in FIG. 4 is simple differential pressure controller450. In the differential pressure controller 450 the rotationallymovable pinion shaft 328 is replaced by an immovable reaction torquefitting 452. In addition to providing an anchor for the lower end of thetorsion bar 213 (via the pin 360), the reaction torque fitting 452comprises the male spline 442 and provides a cylindrical mountingsurface for the ball bearing 338. A handle 454 is mounted on the inputshaft 380. Thus, rotation of the handle 454 is possible within the angle±θ.sub.θ with concomitant linearly related differential output pressureavailable at the first and second output lines 426 and 427,respectively. Again, possible applications are limitless. For instance,such a differential pressure controller could be utilized in an"open-loop" control system for opening or closing a large hydraulicallyactuated valve.

If electro-mechanical or other controllable drive means are substitutedfor the handle 454, a servo-valve is brought into being. For instance,shown in FIG. 5A is an electro-mechanical (i.e., motor driven)servo-valve 460. The electro-mechanical servo-valve 460 is identicalwith the differential pressure controller 450 except that the handle 454has been replaced by an electrically actuated motor 462. Suitableexamples of electrically actuated motors can be found in a line oflimited rotation DC torque motors manufactured by Aeroflex LaboratoriesInc. of Plainview, N.Y.

An alternate preferred embodiment for a limited rotation DC torque motoris shown in FIG. 5B. Shown in FIG. 5B is a torque motor 470. The designof the torque motor 470 is closely related to DC torque motors used by anumber of manufacturers for activation two-stage servo-valves of presentdesign. Usually, such DC torque motors are utilized to position a pilotflapper valve and comprise a motor pivot which is located eccentricallywith respect to the DC torque motor itself. Often such pivots comprise aflexure tube which serves to exclude fluid from the pilot flapper valvefrom the DC torque motor. Typical examples of such DC torque motorcontrolled two-stage servo-valves can be found in a line of servo-valvesmanufactured by Moog Inc. of East Aurora, N.Y.

In the torque motor 470, an armature bar 472 is affixed concentricallyabout the input shaft 380. Thus, the armature bar 472 pivots about pivotpoint 474 which is substantially coincident with the center line of theinput shaft 380. Pole pieces 476 and 478 are mounted upon field magnets480. The field magnets are unidirectionally oriented (magnetically) suchthat the pole piece 476 is north poled and the pole piece 478 is southpoled. A pair of armature coils 482 are provided wherein both of thearmature coils 482 are hooked up in an additive manner so that thearmature bar 472 becomes an electro-magnet whose pole orientation andmagnitude are set by current direction and magnitude in the armaturecoils 482.

Typically, the armature bar 472 is formed from a "soft" magneticmaterial having a tall but narrow hysteresis loop of small area. Thecombined dimensions of the armature bar 472, the field magnets 480 andthe pole pieces 476 and 478 are controlled such that clearance isprovided between the ends of the armature bar and the pole pieces 476and 478 for maximum values of θ.sub.θ.

In operation, a current passing through the armature coils 482 causesone end of the armature bar 472 to be north poled and the other to besouth poled. Then the north poled end of the armature bar 472 isrepelled by the north poled pole piece 476 and attracted by the southpoled pole piece 478. Conversely, the south poled end of the armaturebar 472. Currents in the armature coils 482 (and therefore flux levelsin the armature bar 472) are held to values wherein there is asubstantially linear relationship between current and motor torque.

As noted hereinabove, closed-loop servo systems utilizing the four-waytorque reaction valve 210 to position a mass are stabilized by energyloss associated with motion of the mass. Similarly generated energy losswill also have a stabilizing effect upon systems utilizing hydrauliccircuits controlled by either the differential pressure controller 450or the electro-mechanical servo-valve 460.

Under optimum conditions, suitable energy loss may be generatedindependent from the hydraulic circuits. For instance, an automotivetype shock absorber could be coupled to a load to control oscillationsof a system which comprises one of these hydraulic circuits.Alternately, a damper valve assembly may be introduced into either, orboth, of the first and second output fittings 424 and 425, respectively,or lines 426 and 427, respectively.

An optimum damper valve assembly for this purpose is characterized byhaving a selected hydraulic resistance (hereinafter "resistance")function. In general, a simple orifice having a square law flowcharacteristic wherein pressure drop is proportional to fluid flow rate(hereinafter "flow rate") squared is unacceptable. Its resistancefunction would be determined by

    R.sub.a =P.sub.a /Q.sub.a /10000A.sub.a =(P.sub.a).sup.0.5 /100A.sub.a

where R_(a) is the resistance of the orifice, P_(a) is the pressure drop(hereinafter "pressure") across the orifice, Q_(a) is the fluid flowrate through the orifice, and A_(a) is the area of the orifice. Thus,the resistance of an orifice increases linearly with increasing flowrate.

A damper valve assembly 488 having a selected resistance function isshown in FIG. 6 The damper valve assembly 488 comprises two dampervalves 490, each having nominal one-way flow characteristics. They aremounted side-by-side in bores 491 a valve body 492 and the damper valves490 are oriented therein in reversed flow directions to accommodatetwo-way flow. Each damper valve 490 comprises a set of the followingitems:

An oversize orifice counterbore 494 is formed in the valve body 492. Thecounterbore 494 is selectively filled by a contoured valve member 496.Thus, an annular orifice 498 is formed which has a selected resistancevs. flow characteristic determined by an individually selected contouron the contoured valve member 496 as combined with selected stiffnessand preload of a spring 500 used to retard outward motion of thecontoured valve member 496. The spring 500 is located in a counterbore502 and applies force to a stem 504 of the contoured valve member 496via a washer 506 and a retaining ring 508. Return travel of thecontoured valve member 496 is limited by a disc 510 which is retained ina counterbore 512 in the valve body 492 by a retaining ring 514. Fluidpassage to the annular orifice 498 is effected via holes 516 and 518formed in the disc 510 and valve body 492, respectively, and an annularchamber 520 also formed in the valve body 492.

Shown in FIG. 7 is an alternate damper valve assembly 522 wherein adamper valve 490 is mounted in a bore 524 in a check valve 526 whereinone set of all of the above described counterbores, spring, retainingrings, disc and holes are formed or disposed in similar juxtaposition toa contoured valve member 496. The check valve 526 is urged against aspherical seat 528 formed in a check valve body 530 by a spring 532which is located in a counterbore 534 and applies seating force to thecheck valve 526 via a washer 536 and retaining ring 538.

The damper valve 490 is oriented so that its nominal flow direction isopposite that of the check valve 526. Thus, flow is nominally unimpededin one direction but encounters a resistance R in the other. Utilizingone of the damper valve assemblies 522 in each of output lines 426 and427 enables similar pressures to be maintained in either side of thedouble acting cylinder 352 for similar motions in either direction.

While a single valued resistance value is often chosen as the resistancefunction for a particular design of the damper valve 490, a selectedvariable resistance function may be chosen as well. For instance, shownin FIG. 8 are a set of performance curves for a damper valve 490 whereina resistance function that decreases with respect to motion of thecontoured valve member 496 is used. Resistance function,R(lbs.sec./in.⁵), is illustrated by curve 540 while pressure drop, P_(d)(lbs/in.²), and flow rate, Q_(d) (in.³ /sec.), are illustrated by curves542 and 544, respectively. In FIG. 6, the values shown for R, P_(d) andof assume zero preload of the spring 500 and they are plotted vs.displacement of the contoured valve member 496, X_(d) (mils). Aprocedure for designing a damper valve 490 is illustrated via thefollowing example calculation for a damper valve 490 having theperformance depicted in FIG. 8.

Because the annular orifice 298 has a wedge shaped flow, its flowcoefficient is about 50 percent higher than a sharp edged orifice. Thus,

    Q.sub.d =P.sub.d /R=150A.sub.d (P.sub.d).sup.0.5

where A_(d) is the flow area of the annular orifice 298. Also,

    R=200-5000X.sub.d

and

    A.sub.d =π[(0.47).sup.2 -r.sub.d.sup.2 ]

where X_(d) is a displacement value for the contoured valve member 496and r_(d) is a value representative of a particular radius of thecontoured valve member 496. Also, valve force is determined by

    F.sub.d =K.sub.d X.sub.d =P.sub.d d.sup.πr.sub.d.sup.2

where k_(d) is the spring constant of the spring 500 which is determinedby the relationship

    P.sub.d =400(lbs/in..sup.2) when X.sub.d =20(mils).

When these equations are mutually solved, X_(d) is found by

X_(d) [(20+0.0309P_(d))-(400-1.236P_(d) +(0.01189P_(d))¹.5+(0.000955P_(d))²)⁰.5 ]/1000

and points generating the curves 540, 542 and 544 are evaluated in atranscendental manner. In addition, values of r_(d) are also calculated.These values are plotted as curves 546a and 546b in FIG. 9. At X_(d) =0,the curve 546a has the same value as curve 548 whose value is that ofthe inside radius of the counterbore 494.

However, the above equations assume that all energy loss in the dampervalve 490 is due to kinetic energy loss. Actual loss is partially due toviscous flow energy loss. In fact this form of energy loss is dominantfor very small clearances. For instance, power steering fluid has anabsolute viscosity of 0.0000171 (lb.sec./in.²) at an operatingtemperature of 170(deg.F) and according to a formula presented in a bookentitied HYDRAULIC CONTROL SYSTEMS, by Herbert E. Merritt and publishedby John Wiley & Sons, Inc.

    R'=P.sub.d /Q.sub.d =6μL.sub.d /πr.sub.d c.sub.d

where R' is the resistance of such an orifice and L_(d) is a lengthassociated with a portion of smaller values of c_(d). c_(d), in turn, isthe radial clearance between the curve 548 and a combined curve 550 and546b. The curve 550 is a chosen continuation of the curve 546b whichdesignates contour requirements of the contoured valve member 496 toeffect the values of R shown by the curve 540 in FIG. 8.

The actual contour of the contoured valve member 496 is determined byprogressively taking the values of cd resulting from the differencebetween the curve 548 and the curves 546b and 550 and swinging radiiwith a compass to generate a curve which is then used for the actualcontour. Shown in FIGS. 10A, 10B and 10C are enlarged views of theactual contour of the contoured valve member 496 wherein X_(d) =0(mils),8.9 (mils) and 20.0 (mils), respectively. These are values of X_(d) forwhich Q_(d) =0 (in. ³ /sec.), 1 (ins³ /sec.) and 4 (in. ³ /sec.),respectively.

Open-loop operation of the four-way torque reaction valve 210 augmentedby a particular damper valve assembly 488 having a single valuedresistance of 200 (lb.sec./in.⁵) can be determined by analyzing aschematic circuit 560 shown in FIG. 11. If an effective radius, R_(v),of an effective valve area, A_(v), is chosen equal to 0.4 (in.), then

    F.sub.v =T/0.4

where F_(v) is the force imposed upon the effective valve area, A_(v),and T is the torque imposed upon the input shaft 380.

As illustrated in the schematic circuit 560, a pump unit 559 deliversinput flow rate Q_(s) to a bridge circuit comprising variable resistors568, 570, 572 and 574. In addition, F_(v) is applied to the primary ofan ideal transformer 562 (which has the ratio A_(v) :1) via a terminal561 and the primary of an ideal velocity transformer 564. The idealvelocity transformer 564 converts tangential valve velocity dX_(v) /dtinto valve displacement X_(v) via action of a hypothetical integratingoperational amplifier 566. The valve displacement X_(v) results invariation of values of the variable resistors 568 and 570, whose valuescorrespond to the flow characteristics of the first and second inputcontrol orifices 270 and 272, respectively, and the variable resistors572 and 574, whose values correspond to the flow characteristics of thefirst and second return control orifices 282 and 284, respectively.Output pressure P appears between circuit nodes 576 and 578.

The output pressure P is applied to a circuit comprising a resistor 580that is series connected with a parallel combination of the primary ofan ideal transformer 582 and a capacitor 584, all in parallel with thesecondary of the ideal transformer 562. The ideal transformer 582simulates the area of the piston 350 (which has the ratio A_(p) :1). Theideal transformer 582 transforms pressure applied to the piston 350 intoforce which is applied to an inductor 586 (which has the value M). Thecapacitor 584 simulates the capacitance of the fluid trapped in thecylinder 352 (which has the value C). The ideal transformer 562simulates the effective net valve area (which has the ratio A_(v) :1).The transforming action of the ideal transformer 562 simulates therelation

    P=F.sub.v A.sub.v.

(The above designated circuit elements have the following values in theexamples below: M=0.25 (lb.sec.² /in.), C=0.000025 (in.⁵ /lb), A_(p) =1(in.²) and A_(v) =0.1 (in.²).)

As soon as a circuit becomes more complex than a series or parallelcombination of circuit elements, the simplest way to analyze it is byusing a method known as the Ladder Method, which method is explained inthe book entitied ELECTRICAL ENGINEERING CIRCUITS by Hugh HildrethSkilling and published by John Wiley & Sons, Inc. In utilizing thismethod for the pressure/flow problems herein, a velocity of dX_(m).dt isassumed to flow in the inductor 586. Then the flow rate across theprimary of the transformer 582 is A_(p) (dX_(m) /dt) and the pressuredrop across the primary of the transformer 582 is (jωM/A_(p)) (dX_(m)/dt). This pressure is divided by the impedance of the capacitor 584,(-j/ωC) to determine the flow rate through the capacitor 582 (which is(-1)(ω² MC/A_(p)) (dX_(m) /dt)). These flow rates are then summed andmultiplied by the resistance value of the resistance 580, R, todetermine the pressure drop across the resistor 580. This pressure dropis summed with the pressure drop across the primary of the transformer582 to determine a concomitant value for the output pressure P. This ismultiplied by the effective valve area A_(v) which results in anequation relating (dX_(m) /dt) to F_(v) in terms of R, A_(p), A_(v), ω ,M and C. Finally, the resulting equation is rearranged and theLaplace-transform variable s is applied which results in the blocktransfer function

    X.sub.m /F.sub.v =(1/RA.sub.p A.sub.v)/s[(MC/A.sub.p.sup.2)s.sup.2 =(M/RA.sub.p.sup.2)s+1]

Shown in FIGS. 12A and 12B are Bode diagrams for the gain magnitude andphase angle, respectively, of this block transfer function (as evaluatedby using the circuit values mentioned above). A curve 588 depicts thelog of the magnitude of X_(m) /F_(v) shown in FIG. 28A and a curve 590depicts the concomitant phase angle shown in FIG. 28B.

The torsional stiffness of the torsion bar 213 determines the log (X_(m)/F_(v)) value of the abscissa 592. Shown in FIG. 13 is a simplifiedblock diagram 595 for a closed-loop servo system comprising theclosed-loop system described by the schematic circuit 560 and themechanical features of the four-way torque reaction valve 210. Comprisedin a block 594 is the torsional stiffness value of 400 (in.lb/rad.)selected for the torsion bar 213. Thus, a maximum value of θ.sub.θ =0.1(rad.) results in T-40 (in.lb). The torque value is then divided byR=0.4 (in.) in block 596 to determine a value for F_(v) (yielding amaximum value of F_(v) =100 (lbs) which when divided by A_(v) =0.1(in.²) results in a maximum value of P=1000 (lb/in.²). X_(m) isdetermined via multiplication of X_(m) /F_(v) in block 598, which blockcomprises the above defined block transfer function). X_(m) is fed backvia block 600 whose value is the inverse of the radius of the pinion328, 1/N_(p) =1/0.333 (in.). Finally, the X_(m) /F_(v) value of theabscissa 592 is that value for the block 598 which will result in a loopgain of l. This value is the inverse of the product of the values of theblocks 594, 596 and 600, or 0.000333 (in./lb). Therefore, the abscissa592 is plotted at log (0.000333)=-3.477.

The phase angle associated with unity gain cross-over (at point 602),determines the stability of the closed-loop servo system. This angle isshown (via following lines 604a and 604b) to be -106 (deg.) in FIG. 12B.However, the nature of the curves 588 and 590 at frequencies slightlyhigher than that corresponding to unity gain cross-over 182(rad./sec.)=29.0 (Hz)) suggests that slight changes in gain could leadto stability problems. This problem can easily be corrected by reducingthe torsional stiffness of the torsion bar 213. However, that wouldconcomitantly diminish the other performance parameters of theclosed-loop servo system.

One might be tempted to change the value of R. Increasing the value of Rwould reduce the gain, but would also reduce circuit damping. If carriedfar enough, this would result in the curve 588 having a resonance likecharacteristic. In fact, if R is reduced to near zero values, X_(m)/F_(v) becomes A_(p) /MA_(v) s2 (which equals (-1)(A_(p) /MA_(v) ω²))with a concomitant constant phase angle value of -180 (deg.).

Another way to increase circuit damping is to introduce a "leak" acrossthe primary of the transformer 582. The conductance of such a "lease"would obviously serve to dampen any oscillations of the parallel circuitcomprising the mass 586, transformer 582 and capacitor 584. However,because it would be in series with the resistor 580, it would alsoreduce the maximum pressure available at the primary of the transformer582 and the concomitant maximum force available to move the mass 586.

On the other hand, if a system having more realistic loadcharacteristics is assumed, a non-linear resistor, such as an orificewhose resistance is R_(b) =(P_(b))⁰.5 /100A_(b), may be utilized as the"leak". The increasing resistance, with respect to pressure, of such anorifice limits the loss of maximum force available to move the mass 586.For instance, consider a system having a load characterized by

    F=F.sub.o K.sub.a X.sub.m +.sub.b (dX.sub.m /dt)

where F is a load force encountered by the mass 586 whenever it moves,F_(o) is a coulomb (friction) force component of the load force, K_(a)is a load spring constant (i.e., such as the restoring caster anglederived force encountered by a vehicular steering system), and K_(b) isa load damping constant (i.e., such as encountered by scrubbing softrubber against an abrasive surface). The nature of such a load forcepermits an orifice 606 as shown in FIG. 14 to be utilized anywhere inparallel with the primary of the transformer 582. As shown in FIG. 14,one convenient location for mounting the orifice 606 is in a hole 608formed in the piston 350.

Shown in FIG. 15 is a schematic circuit 610 which has been modified toinclude a block 612 comprising the load force F and a variable resistor614 depicting the variable resistance of the orifice 606. The schematiccircuit 610 is analyzed generally in the same manner as the schematiccircuit 560. However, the pressure drop across the primary of thetransformer 582 is now (jωM/A_(p))(dX_(m) /dt)+(F/A_(p)) and the flowrate through the capacitor 584 is now (-1)(ω² MC/A_(p))(dX_(m)/dt)+(C/A_(p))(dF/dt). The function (dF/dt) can be found via theequation

    dF/dt=K.sub.a (dX.sub.m /dt)+K.sub.b (d.sup.2 X.sub.m /dt.sup.2).

In addition, there is a parallel flow rate through the variable resistor614 of (jωM/R_(b) A_(p))(dX_(m) /dt)+F/R_(b) A_(p).

Because of the K_(a) dX_(m) term in the load force F, the system is nolonger a so called type 1 system. That is, the denominator of aresulting block transfer function is no longer multiplied by theLaplace-transform variable s to the first power. The practical result ofthis is that there will be a residual steady state error in X_(m) andconcomitant non-zero steady state values of F and P. For this reason andfor the reason that some persons skilled in the art may not be familiarwith Laplace-transformations, the resulting equations for determiningthe gain magnitude and phase angle of a new block transfer function arepresented as follows:

    X.sub.m /[F.sub.v -((R+R.sub.b)A.sub.v F.sub.o /R.sub.b A.sub.p)]=(1/RA.sub.p A.sub.v)/

     [(K.sub.a (R+R.sub.b)/RR.sub.b A.sub.p.sup.2)-(((R+R.sub.b)M/RR.sub.b A.sub.p.sup.2)+(K.sub.b C/A.sub.p.sup.2))ω.sup.2

     +jω(1+(K.sub.a C/A.sub.p.sup.2)+(K.sub.b (R+R.sub.b)/RR.sub.p A.sub.p.sup.2)-(MCω.sup.2 /A.sub.p.sup.2))]

    and

    f=-tan .sup.-1 [1+(K.sub.a C/A.sub.p.sup.2)+(K.sub.b (R+R.sub.b)/RR.sub.b A.sub.p.sup.2)-(MCω.sup.2 /A.sub.p.sup.2)]ω/

     [(K.sub.a (R+R.sub.b)/RR.sub.b A.sub.p.sup.2)-(((R+R.sub.b)M/RR.sub.b A.sub.p.sup.2)+(K.sub.b C/A.sub.p.sup.2))ω.sup.2 ],

respectively.

Steady state values of these equations can be evaluated by setting (ω=0.When the relation T=0.4 F is included, the following equations describetorque and phase angle as a function of K_(a), R, R_(b), A_(p), A_(v),F_(o) and X_(m) under steady state conditions:

    T=0.4[(R+R.sub.b)A.sub.v /R.sub.b A.sub.p ](F.sub.o +K.sub.a X.sub.m)

    and

    f=0.0(rad.),

respectively.

Most of the circuit values previously mentioned are used in evaluatingthe above equations, including M=0.25 (lb.sec.² /in.), C=0.000025 (in.⁵/lb.), A_(p) =1 (in.²) and A_(v) =0.1 (in.²). However, K_(a), K_(b), Rand R_(b) may vary as a function of load conditions. Shown in FIG. 16 isa curve 615 which depicts output force/torque vs. torque for K_(a) =100(lb./in.), R=200 (lb.sec./in.⁵) and R_(b) =63.25 (F/A_(p) ²)0.5(lb.sec./in.⁵) where the output force, F, equals the sum, F_(o) +K_(a)X_(m).

(This value for R_(b) requires an orifice sized via the followingprocedure:

    R.sub.b =(1/A.sub.p.sup.2)(dF/dQ.sub.b)=[dQ.sub.b.sup.2 /10000A.sub.b.sup.2)/dQ.sub.b

     =[Q.sub.b /5000A.sub.b.sup.2 ]=[100A.sub.b (F/A.sub.b.sup.2).sup.0.5 /5000A.sub.b.sup.2 ],

    thus

    63.25(F/A.sub.p.sup.2)0.5=(0.02/A.sub.b)(F/A.sub.p.sup.2).sup.0.5,

    or

    A.sub.b =(0.02/63.25)=0.000316 (in..sup.2),

    and

    d.sub.b =0.0226 (in.)

where d_(b) is the diameter of the orifice 606.

Shown in FIGS. 17A and 17B are Bode diagrams for the gain magnitude andphase angle, respectively, of the new block transfer function for thefollowing assumed values for K_(a), K_(b), R and R_(b) which correspondto F 10 (lbs.), 100 (lbs.) and 1000 (lbs.) and near zero values ofdX_(m) /dt: K_(a) =100 (lbs./in.); K_(b) =10 (lb.sec./in.), 20(lb.sec./in.) and 40 (lb.sec./in.), respectively; R=200 (lb.sec./in.⁵),632.5 (lb.sec./in.⁵) and 2000 (lb.sec./in.⁵), respectively. In FIGS. 17Aand 17B, curves 616a and 616b, 618a and 618b, and 620a and 620bcorrespond to F=10 (lbs.), 100 (lbs.) and 1000 (lbs.), respectively.

Shown in FIGS. 18A and 18B are Bode diagrams for the gain magnitude andphase angle, respectively, of the new block transfer function for thefollowing assumed values for K_(a), K_(b), R and R_(b) which correspondto F=1000 (lbs.) and dX_(m) /dt=0 (in./sec.), 1 (in./sec.) and 4(in./sec.): K_(a) =100 (lbs./in.); K_(b) =40 (lb.sec./in.), 80(lb.sec./in.) and 160 (lb.sec./in.), respectively; R=200 (lb.sec./in.⁵),150 (lb.sec./in.⁵) and 100 (lb.sec./in.⁵), respectively, and R_(b) =2000(lb.sec./in.⁵). In FIGS. 18A and 18B, curves 622a and 622b, 624a and624b, and 626a and 626b correspond to dX_(m) /dt=0 (in./sec.), 1(in./sec.) and 4 (in./sec.) respectively. All of the curves shown inFIGS. 17A, 17B, 18A and 18B depict stable operation with very acceptablephase angles and margins of error.

FIG. 19 is a flow chart that outlines the procedure followed incontrolling a closed-loop servo system comprising a four-way torquereaction valve 210. Fluid is supplied to the four-way torque reactionvalve 210 via input line 410. Torque is applied to input shaft 380 whichcauses outer valve member 214 to rotate. Non-zero output pressure isgenerated and applied to a utilization device. The utilization devicegenerates an output force which (in general) results in movement of theutilization device. The movement of the utilization device causescounter-rotation of pinion shaft 328 and the lower end of torsion bar213. The output pressure also causes inner valve member 212 torotate--which causes rotation of the upper end of the torsion bar 213.Combined counter-rotation of its lower end and rotation of its upper endcauses the torsion bar 213 to twist by θ.sub.θ. The twisting of thetorsion bar 213 maintains tactile torque feedback (to the input shaft380) which is proportional to θ.sub.θ (and therefore proportional to theoutput pressure).

FIG. 20 is a flow chart that outlines the procedure followed incontrolling an open-loop servo system comprising a differential pressurecontroller 450. Fluid is supplied to the differential pressurecontroller 450 via line 410. Torque is applied to input shaft 380 whichcauses outer valve member 214 to rotate. Non-zero output pressure isgenerated and applied to a utilization device. The utilization devicegenerates an output force. The output pressure also causes inner valvemember 212 to rotate--which causes rotation of the upper end of thetorsion bar 213. The rotation of its upper end causes the torsion bar213 to twist by θ.sub.θ. The twisting of the torsion bar 213 maintainstactile torque feedback (to the input shaft 380) which is proportionalto θ.sub.θ (and therefore proportional to the output pressure).

FIG. 21 is a flow chart that outlines the procedure followed incontrolling a servo system (either open or closed-loop) comprising anelectro-hydraulic servo valve 460. Fluid is supplied to theelectro-hydraulic servo valve 460 via input line 410. A power signal isapplied to motor 462 which exerts torque on input shaft 380. This causesouter valve member 214 to rotate. Non-zero output pressure is generatedand applied to a utilization device. The utilization device generates anoutput force. The output pressure also causes inner valve member 212 torotate on pinion shaft 328 and the lower end of torsion bar 213. Theoutput pressure also causes inner valve member 212 to rotate--whichcauses rotation of the upper end of the torsion bar 213. The rotation ofits upper end causes the torsion bar 213 to twist by θ.sub.θ. Thetwisting of the torsion bar 213 maintains feedback torque to the motor462 (via the input shaft 380) which is proportional to θ.sub.θ (andtherefore proportional to the output pressure).

Shown in FIG. 22A is a longitudinal section view (whose top and bottomhalves are taken along selected sections as described below) of a handoperated pressure controller 710 which is operationally similar to thedifferential pressure controller 450 shown in FIG. 4. Because the outervalve member 214, which comprises various hydraulic slip rings and theirconcomitant seal rings 439, is directly coupled to the input shaft 380of the differential pressure controller 450, it has been found thatexcessive torque can be required for its operation when system pressuresare high. Thus, the hand operated pressure controller 710 comprises aconvoluted design wherein its inner valve member 711 is directly coupledto its input shaft 712 and its outer valve member 713 is directlycoupled to its valve body 714.

The inner valve member 711 and outer valve member 713 function in thesame manner as the inner and outer valve members 212 and 214,respectively, in the torque reaction valve 210 or the inner and outervalve members 262 and 264, respectively, in the torque reaction valve260. If they emulate the inner and outer valve members 262 and 264,respectively, they are configured as shown in FIGS. 23A and 23B,respectively, and fabricated in the manner of external and internalgears, respectively, as described above.

Disposed within the lower end of the valve body 714 is an anchor shaft715 with a locating key 716. It is located therein by a bore 717,shoulder 718 and keyway 719 formed in the valve body 714 whereat it isretained by a nut 720 and washer 721. The lower end of the input shaft712 is supported for rotation within the anchor shaft 715 and about abearing pin 722 by a bushing 723. The bearing pin 722 is secured withinthe anchor shaft 715 via a knurled portion 724 pressed into a bore 725formed in the anchor shaft 715. Excessive rotation of the input shaft712 is precluded in a known manner via action of a loose meshing splinesection 726 whose external teeth 727 are formed in the input shaft 712and internal teeth 728 are formed in the anchor shaft 715. To eliminatelater assembly problems, the number of teeth comprised in the loosemeshing spline section 726 is chosen to be an integer multiple of thenumber of slot sets formed in the inner and outer valve members 711 and713, respectively, as also described above.

The outer valve member 713 is pressed into a bore 729 of a valve sleeve730 until it is seated against a shoulder 731 thereof to form an outervalve assembly 732. The outer valve assembly 732 is precluded fromrotation within the valve body 714 by a pin 775 protruding through ahole 776 formed in the valve sleeve 730. The pin 775 is disposed in afixed location with respect to the valve body 714 because it is pressedinto a hole 777 formed in the anchor shaft 715 which is precluded fromrotation in the valve body 714 by the locating key 716.

Input and output hydraulic slip rings 733 and 734, respectively, andseal rings 735 are provided--also in a known manner. After the outervalve member 713 is pressed into the valve sleeve 730, multiple inputand output ports 736, and 737a and 737b, respectively, are formed in theouter valve assembly 732 to allow fluid to flow from the input hydraulicslip ring 733 to input slots 738, and to or from the output hydraulicslip ring 734 from (or to) either sets of output slots 739a or 739b,respectively, (Note that the top and bottom halves of FIG. 22A are takenalong sections comprising the input ports 736 and the output ports 737,respectively.)

Shown in FIGS. 24A and 24B are a damper valve 740 and a check valve 741,respectively. They are constructed in substantially the manner describedabove with respect to the damper valve 490 and check valve 526subassemblies of the damper valve assembly 522 shown in FIG. 7. As shownin FIG. 22B, they are threadably assembled into first and second outputflow passage legs 742a and 742b, respectively, formed in the valve body714. The output flow passage legs 742a and 742b communicate directlywith either of the output hydraulic slip rings 734 and fluid flowtherefrom flows without restriction to output passageway 743 and outputline 744 via the check valve 741. Returning fluid flow to the outputpassageway 743 must flow through the damper valve 740, however, issubject to resistive pressure drop which is a function of its flow rateas described hereinabove.

Pressurized fluid is supplied via input line 773 and input port 774 andsubjects the input slots 738 and one of the sets of output slots 739a or739b to pressurized fluid. The pressurized fluid contained therein isnominally sealed by the shoulder 731 and either of barrier rings 745shown in FIG. 25A or 746 shown in FIG. 25B. The barrier rings 745 and746 are formed with a set of holes 747. The holes 747 are aligned withreturn slots 748 (formed in the outer valve member 713) during assemblyvia alignment of a pin 749 (pressed into the outer valve member 713) anda hole 750 formed in the barrier ring 745. The barrier ring 745 isforceably held against outer end 751 of the outer valve member 713 by abeveled internal retaining ring 752 as shown in FIG. 22A. To facilitateunconstrained rotational motion of the inner valve member 711--combinedwith adequate sealing of pressurized fluid--the inner valve member 711is formed axially slightly shorter than the outer valve member 713.Representative differences in axial length range between 0.0002 (in.)and 0.0006 (in.). Thus, the inner valve member 711 is constrainedaxially and in pitch and yaw by the shoulder 731 and either of thebarrier rings 745 or 746 while it is constrained in either radialdirection by an internal circumferential rib 778 formed therein.

The input shaft 712 is located radially by a bearing assembly 753comprising a drawn cup needle bearing 754 mounted in a ring 755 andaxially in a known manner by retaining rings 756 loosely bearing againstthe drawn cup needle bearing 754. Fluid is sealed within the handoperated pressure controller 710 by a seal assembly 757 also formed in aknown manner. The ring 755 and the seal assembly 757 are forceablyretained within the valve body by an internal retaining ring 758.

Torque inputs to the hand operated pressure controller 710 are made viatangential force applied to a handle 759 by an operator. The handle 759is clamped onto the input shaft 712 via a bolt 760 in a known manner.Input torque is transmitted to the inner valve member via a torsion bar761 as indicated in FIG. 26. Torque is transmitted to the torsion bar761 from the input shaft 712 via a pin 762 in a known manner. Thetorsion bar 761 undergoes torsional deflection which is proportional tothe impressed torque thereby availing the operator suitable tactileresponse. The torque is then transmitted to the inner valve member 711via a pin 763 whose notched ends 764 engage radial slots 765 formed inthe inner valve member 71 1. The purpose of shoulders 766 (formed vianotching the pin 763) is to limit radial displacement of the pin 763 sothat it can not contact the outer valve member 713 and interfere withunconstrained rotational motion of the inner valve member 711.

Utilizing the barrier ring 745 serves to configure the hand operatedpressure controller 710 as a four-way hand operated pressure controller767. This is because both sets of output slots 739a and 739b are sealedby the shoulder 731 and barder ring 745. This requires the use of twosets of damper valves 740, check valves 741 output flow passage legs742a and 742b, output passageways 743 and output lines 744. The four-wayhand operated pressure controller 767 operates in precisely the samemanner as the differential pressure controller 450.

Utilizing the barrier ring 746 serves to configure the hand operatedpressure controller 710 as a three-way hand operated pressure controller768. This is because another set of holes 769 is used to deactivate theset of output slots 739b by relieving fluid pressure therein directly tovalve body chamber 770. All return fluid is conducted therefrom toreturn port 771 and return line 772. Thus, only one set of damper valve740, check valve 741 output flow passage legs 742a and 742b, outputpassageway 743 and output line 744 is required.

Shown in FIG. 27 is a is an electro-mechanical servo-valve 780. Theelectro-mechanical servo-valve 780 is identical with the hand operatedpressure controller 710 except that the handle 759 has been replaced byan electrically actuated motor 781. The electrically actuated motor 781can comprise the torque motor 470 shown in FIG. 5B. If the barrier ring745 is utilized in the electro-mechanical servo-valve 780, then it isconfigured as a four-way electro-mechanical servo-valve 782--whichoperates in precisely the same manner as the electro-mechanicalservo-valve 460. If the barrier ring 746 is utilized in theelectro-mechanical servo-valve 780 then it is configured as a three-wayelectro-mechanical servo-valve 783.

Shown in FIG. 28 is a torque reaction valve 800 which is functionallyequivalent to either of the torque reaction valves 210 or 260. However,it also comprises substantially all of the inner components describedabove with respect to the hand operated pressure controller 710.However, the inner components of the torque reaction valve 800 rotate ina "follow-along" manner with respect to a piston/rack assembly 801 of apower steering system 802 within which the torque reaction valve 800 iscomprised. Substantive differences between the torque reaction valve 800and the hand operated pressure controller 710 comprise the following:

The anchor shaft 715 is replaced with a rotating pinion shaft 803 whichcomprises a pinion gear 804 that meshes with rack gear teeth 805 formedon the piston/rack assembly 801. The piston/rack assembly 801 isforceably urged toward the pinion gear 804 by a spring loaded yoke 806in a known manner so that the mesh between the pinion gear 804 and therack gear teeth 805 is backlash free. Thus, the outer valve assembly 732is constrained to rotate proportionally to transversing (i.e., in andout of the plane of FIG. 28) motions of the piston/rack assembly 801.The pinion shaft 803 is located with respect to a steering gear/valvebody 807 in a known manner by a bearing 808, nut 809, a beveled internalretaining ring 810 and a bushing 811. Gear lubricant is contained in achamber 812 comprising the pinion gear 804 and rack gear teeth 805 by acap 813 and a shaft seal 814 in a known manner. The shaft seal 814 alsoserves to keep hydraulic fluid from migrating into the chamber 812 froma chamber 815 comprising the inner components of the torque reactionvalve 800.

Shown in FIG. 29 is a torque reaction valve 816 which additionallycomprises a feedback torsion bar 817a. The feedback torsion bar 817a isactually formed as a portion of a new torsion bar 817 which also servesboth the function of the torsion bar 761 and the bearing pin 722. Thus,the new torsion bar 817 comprises the feedback spring 817a, a torsionbar 817b and a bearing pin 817c. Incipient torque levels applied via theinput shaft 712 are directly applied to the pinion shaft 803 via thetorsion bar 817--before the inner valve member 711 moves substantiallywith respect to the outer valve member 713. In fact, applied torque isbifurcated between the feedback spring 817a and reaction interface ofthe inner and outer valve members 711 and 713, respectively. Thetorsional spring stiffness of the reaction interface (i.e., valvetorsional stiffness K_(v)) is

    K.sub.v =R.sub.v A.sub.v Q.sub.s.sup.2 /45000L.sub.ve.sup.2 (X.sub.o -X.sub.v).sup.3,

where R_(v) is valve radius, A_(v) is valve area, Q_(s) is fluid supplyflow rate as described hereinbefore, L_(ve) is effective valve length,X_(o) is nominal tangential valve clearance and X_(v) is tangentialvalve motion.

In addition, because the pin 763 must be rotationally indexed withrespect to the pinion shaft 803, the inner and outer valve members 711and 713, respectively, are rotationally centered with respect to oneanother and then a hole 818 formed to receive the pin 775. Alternately,a pin 819 can be used to anchor the new torsion bar 817 (instead of thepress fit described hereinabove). Thus, the required rotational indexingcan be accomplished via assembly of either the pin 775 or the pin 819.

Also, because the input shaft 712 is axially constrained with respect tothe new torsion bar 817 via assembling pin 762, it is thereby axiallyconstrained with respect to the steering gear/valve body 807 via thepinion shaft 803 and the bearing 808. Thus, there is no requirement forthe retaining rings 756 in the torque reaction valve 816.

Shown in FIG. 30A is a block diagram 820 depicting operation of a powersteering system which incorporates either of the torque reaction valves800 or 816. Shown in FIG. 30B is an output section block diagram 821which is pertinent to understanding the block diagram 820. The blockdiagram 821 depicts the operational characteristics of a host vehicle'sstructure, wheels, tires and tire patch wherein tire patchcharacteristics include

    K.sub.tp =15000e.sup.-1.5X p

    and

    B.sub.tp =500+1000X.sub.p +175X.sub.p.sup.2,

where k_(tp) is tire patch stiffness, X_(p) is piston/rack assemblymotion and B_(tp) is tire patch damping coefficient for a sample tirepatch.

The output signal of a steering system as a whole determines the averagesteering angle achieved at the host vehicle's tire patches, θ_(tp),which is located in the block diagram 821 at output terminal 822. θ_(tp)is determined by the sum of the torques applied to the tire patches,T_(tp) (located at terminal 823), multiplied by control element1/(B_(tp) s+K_(tp)) shown at block 824. T_(tp) is determined by thedifference between average dirigible wheel angle, θ_(w), and θ_(tp)(which difference is achieved via summing point 825), multiplied bycontrol element (B_(sw) s+K_(sw)) (side wall damping and spring rateterms, respectively) shown at block 826--plus any disturbing torque (asshown at summing point 827). θ_(w) is determined by the differencebetween the sum of the torques applied to the wheels, T_(w), and T_(tp)(which difference is achieved via summing point 828), multiplied bycontrol element 1/(J_(w) s²) (wheel moment of inertia term) shown atblock 829. T_(w) is determined by the sum of the forces applied to wheellever arms, F_(r) (located at terminal 830), multiplied by a controlelement R_(w) shown at block 831. F_(r) is determined by the differencebetween the position of a rack of the host steering system, X_(r) =X_(t)(located at terminal 832), and θ_(w) multiplied by another controlelement R_(w) shown at block 833 (which difference is achieved viasumming point 834), multiplied by control element (overall stiffness ofthe host vehicle's structure--including its tie rod assembly).

The principle function of a host steering system is to determine X_(p).It is not able to do this independently from the elements of the outputsection 821. This is because F_(r) is fed back from terminal 818 to aposition located within the host steering system. In the block diagram820 this occurs at summing point 835 which is located within controlsection 836.

Inputs to the control section 836 are made at input terminal 844 byapplying torque, T_(s), to the host vehicle's steering wheel (notshown). Torque present at an input shaft of the torque reaction valve,T, is subtracted therefrom (which subtraction is performed by summingpoint 845). The product of (T_(s) -T) and control element 1/(J_(s) s²+B_(s)) shown at block 846 determines steering wheel angle θ_(s). Theproduct of X_(p) and control element 1/N_(p) shown at block 847determines rotational position feedback angle θ_(f). The differencebetween θ_(s) and θ_(f), which difference is generated by summing point848, generates the sum of a steering shaft twist angle θ_(sc) and asystem input error angle (θ_(e) +θ_(v)) (where θ_(v) is a displacementangle of the inner valve member 711 with respect to the outer valvemember 713). The product of (θ_(sc) +θ_(e) +θ_(v)) and control elementK_(sc) /(K₁ +K_(sc)) (where K₁ =K_(t) (K_(v) +K_(f))/(K_(t) +K_(v)+K_(v)), and K_(t), K_(v) and K_(f) are torsion bar stiffness, the valvetorsional stiffness and feedback spring stiffness, respectively) shownat block 849 generates the system input error angle (θ_(e) +θ_(v)) whichcomprises a twist angle of the torsion bar plus a valve orificedisplacement angle (i.e., inner valve member rotation with respect tothe outer valve member). The product of (θ_(e) +θ_(v)) and controlelement K₁ shown at block 850 provides the torque T.

Mechanically derived steering force, F_(m), is provided by the productof T and control element 1/N_(p) shown at block 851. Hydraulicallyderived steering force, F_(p), is provided via a product of T and astring of control elements as follows: T multiplied by control elementK₂ /R_(v) (where K₂ =K_(v) /(K_(v) +K_(f)) and R_(v) is valve radius)shown at block 852 generates tangential valve force F_(v). F_(v)multiplied by control element 1/(τs+1)A_(v) (where t is fluid supplytime constant, s is Laplace complex variable and A_(v) is valve reactionarea) shown at block 853 generates valve output pressure P_(v). Pistonpressure P_(p), is generated as follows:

The product of X_(p) and control element As (product of piston area andLaplace complex variable) shown at block 854 determines cylinder flowrate Q_(p). Q_(p) subtracted from the product of P_(p) and controlelement (K_(c) s+L_(p)) shown at block 855 (which subtraction isperformed at summing point 856) determines net valve flow rate Q_(v).The product of Q_(v) and control element R (damper valve resistance asdescribed hereinabove) shown at block 857 is subtracted from P_(v) atsumming point 858 to generate P_(p). The product of P_(p) and controlelement A shown at block 859 generates hydraulically derived steeringforce F_(p). F_(p), is summed with F_(m) at summing point 860 togenerate total steering force F_(t). F_(r) (from the block diagram 821)is subtracted from F_(t) at summing point 835 to generate net steeringforce F. And finally, F multiplied by control element 1/(M_(p) s² +B_(p)s) shown at block 862 generates X_(p).

Shown in FIG. 31 is a "canonical form" block diagram 870. The blockdiagram 820 can be reduced to this format via computation of suitableforward and feedback transfer functions. In the block diagram 870 aninput signal, I, is applied to input terminal 871. Closed-loop responseof the block diagram 870 yields an output signal, C, at output terminal872. C multiplied by control element H shown at block 873 generates afeedback signal, B, which appears at feedback terminal 874. B issubtracted from I at summing point 875 to generate an error signal, E.Finally, E multiplied by control element G shown at block 876 generatesthe output signal C.

It is desirable for the power steering system represented by the blockdiagram 870 to operate in a stable manner. This will occur if theabsolute value of an open-loop transfer function comprising the productGH goes through the value 1 with the absolute value of its argument lessthan 180(deg.). If this is true then any disturbing signal input to thesystem will be damped out and the system's operation will be stable.

Two forms of open-loop transfer function can be defined with respect tothe block diagram 820. A first open-loop transfer function, GH, relatesX_(p) to T_(s). It is of interest to plot this function with respect tofrequency and phase angle in order to judge system stability. A secondopen-loop transfer function, GoHo, relates X_(p) to θ_(s). Because lowfrequency values differ widely between these two functions, it is ofinterest to plot real and imaginary parts of ratios of tire patchrotation θ_(tp) to T_(s) and θ_(s), respectively, (In the case of T_(s)it is also helpful to multiply by a normalizing function such as acontrol element Q₉ =J_(s) s² +B_(s) s.) In an ideal power steeringsystem, plots of these ratios would be resonance free and have theirmaximum values at 0.0(Hz).

Detailed analysis and plotting of these functions is greatly aided byutilizing sophisticated computer analysis techniques. Such analysis hasbeen performed herein on a Macintosh computer with an analysis programentitled MATHEMATICA (which program is available from Wolfram Research,Inc. of Champaign, Ill,). Shown below are typical values for the variousterms defined above. These values comprise input data for particularprograms which were used to analyze a torque reaction valve equippedpower steering system. In these programs lower case letters and nosubscripts are used. Thus, js is understood to represent J_(s) and soon. The first program is used to plot output (steering) force ft as afunction of xv. The second program is used to plot system performancefor a particular chosen value of xv. The first program is defined asfollows:

    ______________________________________                                        xo = 0.004;                                                                   kt = 640.0;                                                                   ks = 0.0;                                                                     kf = 0.0;                                                                     lve = 1.5;                                                                    rv = 0.55;                                                                    av = 0.05;                                                                    qs = 6;                                                                       lp = 0.0001;                                                                  r = 200;                                                                      tv[xv.sub.-- ]:= rv av qs 2/(90000 lve 2 (xo - xv) 2);                        ts[xv.sub.-- ]:= tv[xv] + kf xv/rv;                                           kv[xv.sub.-- ]:= rv av qs 2/(45000 lve 2 (xo - xv) 3);                        k2[xv.sub.-- ]:= kt kv[xv]/(ks (kt + kv[xv] + kf) +                            kt (kv[xv] + kf));                                                           np = 0.333333;                                                                fm[xv.sub.-- ]:= ts[xv]/np;                                                   a = 1.0;                                                                      fp[xv.sub.-- ]:= tv[xv] a/(rv av (1 + rlp));                                  ft[xv.sub.-- ]:= fm[xv] + fp[xv];                                             thetae[xv.sub.-- ]:= ts[xv]/kt;                                               thetav[xv.sub.-- ]:= xv/rv;                                                   thetas[xv.sub.-- ]:= thetae[ xv] + thetav[xv];                                ______________________________________                                    

Shown in FIGS. 32A-C are curves 878a-c, respectively which depict theoutput force ft as a function of T_(s), X_(v) and q_(s), respectively,via utilization of the above values. Since kf=0.0 in the above values,the curves 878a-c depict the output force for a power steering systemutilizing the torque reaction valve 800. Shown in FIGS. 33A-C are curves879a-c, respectively, which depict the output force ft as a function ofT_(s), X_(v) and θ_(s), respectively, for a modified set of valueswherein kf=960(in.lb.). Thus, the curves 879a-c depict the output forcefor a power steering system utilizing the torque reaction valve 816.

The second program is defined as follows: (Note: This set of valuesincludes a particular chosen value of xv=0.001 (in.). In general, anyvalue of xv less than 0.004(in.) may be used so long as it results in anft value less than 400(lbs.))

    ______________________________________                                        xv = 0.001;                                                                   xo = 0.004;                                                                   js = 0.32;                                                                    bs = 0.0;                                                                     ksc = 3200.0;                                                                 kt = 640.0;                                                                   ks = 0.0;                                                                     lve = 1.5;                                                                    rv = 0.55;                                                                    av = 0.05;                                                                    qs = 6;                                                                       lp = 0.0001;                                                                  r = 100;                                                                      tv = rv av qs 2/(90000 lve 2 (xo - xv) 2);                                    ts = tv + kf xv/rv;                                                           kv = rv av qs 2/(45000 lve 2 (xo - xv) 3);                                    k1 = kt (kv + kf)/(kt + kv + kf);                                             k2 = kv/(kv + kf);                                                            k4 = ksc/(ksc + k1)                                                           np = 0.333333;                                                                fm = ts/np;                                                                   a = 1.0;                                                                      fp = ts a/(rv av (1 + rlp));                                                  ft = fm + fp;                                                                 xp = -Log[1 - ft/400]/1.5;                                                    ktp = 15000.0 E (-1.5 xp);                                                    btp = 500 + 1000 xp + 175 xp 2;                                               ksw = 25000.0;                                                                bsw = 100.0;                                                                  jw = 6.25;                                                                    rw = 5.0;                                                                     kr = 4000.0;                                                                  mp = 0.025;                                                                   bp = 2.0;                                                                     q1[s.sub.-- ]:= bsw s + ksw;                                                  q2[s.sub.-- ]:= (btp + bsw) s + ktp + ksw;                                    q3[s.sub.-- ]:= jw s 2 + q1[s] - q1[s] 2/q2[s] + kr rw 2;                     q4[s.sub.-- ]:= mp s 2 + bp s + kr;                                           tau = 0.05;                                                                   kc = 0.000025;                                                                pi = N[Pi, 10];                                                               q5[s.sub.-- ]:= tau s + 1;                                                    q8[s.sub.-- ]:= js s 2 + bs s + k1 k4;                                        q9[s.sub.-- ]:= js s 2 + bs s;                                                q10[s.sub.-- ]:= 1 + r (kc s + lp);                                           q11[s.sub.-- ]:= q1[s] kr rw/(q2[s] q3[s]);                                   go[s.sub.-- ]:= Block[{myq3,myq4,myq5,myq10},                                 myq3 = q3[s];                                                                 myq4 = q4[s];                                                                 myq5 =  q5[s];                                                                myq10 = q10[s];                                                               N[k4 (k1/np + k1 a/(myq5 myq10 rv av))/                                        (myq4 - (kr rw) 2/myq3 + r a 2 s/myq10),                                      10]];                                                                        ho = N[1/np , 10];                                                            g[s.sub.-- ]:= Block[{myq3,myq4,myq5,myq8,myq10},                             myq3 = q3[s];                                                                 myq4 = q4[s];                                                                 myq5 = q5[s];                                                                 myq8 = q8[s];                                                                 myq10 = q10[s];                                                               N[k4 (k1/np + k1 a/(myq5 myq10 rv av))/                                        (myq8 (myq4 - (kr rw) 2/myq3 +                                                r a 2 s/myq10)) , 10]];                                                      h[s.sub.-- ]:= N[q9[s]/np , 10];                                              (*qtp(mrad) q9/ts = 1000 q11 g/(1 + g h) and                                   qtp(mrad)/0s = 1000 q11 go/(1 + go ho)*)                                     ______________________________________                                    

(A thorough explanation of the syntax and other conventions used in theabove programs can be found in a book entitled MATHEMATICA by StephenWolfram and published by Addison-Wesley. Also, an explanation of theprocedures followed in obtaining these plots can be found therein.)

Shown in FIGS. 34A-H are plots depicting Log[Abs[GH], Log[Abs[GH]] as afunction of Arg[GH] (usually known as a Nichols Plot), Re[θ_(tp)Q9/T_(s) ], Im[θ_(tp) Q9/T_(s)), Re[θ_(tp) /θ_(s) ], Im[θ_(tp) /θ_(s) ],R_(s) and X_(s) (where R_(s) and X_(s) are the real and imaginary parts,respectively, of a steering wheel impedance Z_(s) =T_(s) /q_(s) s),respectively, for X_(v) =0.0015(in.)--for a power steering system whichuses the torque reaction valve 800. The selected value X_(v)=0.0015(in.) results in F_(t) =30.5(lbs). Curve 880a in FIG. 34A depictsGH for low frequencies to approximately 4.5(Hz) while curve 880b depictsGH for high frequencies greater than approximately 4.5(Hz). The curve isdiscontinuous because of a sharp resonance in the term (myq4-(kr rw)2/myq3+r a 2 s/myq 10). Similarly, curve 882a in FIG. 34B depicts GH forlow frequencies to approximately 4.5(Hz) while curve 882b depicts GH forhigh frequencies greater than approximately 4.5(Hz). This curve is alsodiscontinuous because of the sharp resonance in the term (myq4-(kr rw)2/myq3+r a 2s/myq10). In fact, it is subject to a jump of --180(deg.) atthe resonance as shown by straight line 882c.

Curve 884 in FIG. 34C depicts Re[θ_(tp) Q9/T_(s) ] while curve 886 inFIG. 34D depicts Im[θ_(tp) Q9/T_(s) ]. They clearly depict a nominallycritically damped resonance at approximately 0.6(Hz). The reason forthat can be seen in curves 880a and 882a whereat Log[Abs[GH]] equalszero. At that value (where Log[w]has a value of about 0.6) Abs[GH]=1.0and has a phase angle of about +120 (deg.)--or a value that isreasonably close to (-1)⁰.5. Thus, even though the curve 882a is to theright of the origin, conditions depicted in the curves 884 and 886 arepresent.

On the other hand, curves 888 and 890 depicting Re[θ_(tp) /θ_(s) ] andIm[θ_(tp) /θ_(s) ], respectively, in FIGS. 34E and 34F, respectively,are near ideal. Thus, a power steering system equipped with the torquereaction valve 800 will be accurately positioned but present a tactiletorque lag at low frequency. While this lag is undesirable, lit ishighly preferable to a resonance which occurs in manual and other typesof power steering systems at about the same frequency.

Real and imaginary parts R_(s) and X_(s), respectively, of the steeringwheel impedance Z_(s) =T_(s) /θ_(s) s are plotted in FIGS. 34G and 34H,respectively. This is accomplished by plotting real and imaginary partsof the expression totable/(ttable I wtable) via the Mathematica programas curves 892 and 894, respectively. These curves comprise a tactilefeel that is quite acceptable. R_(s) is slightly positive which isdesirable for a stable tactile feel. X_(s) is modestly spring-like atvery low frequencies (i.e., less than about 0.5(Hz)) and then (viabecoming positive) becomes inertia like and increases in value as adepiction of the steering wheel moment of inertia.

Shown in FIGS. 35A-H are plots depicting Log[Abs[GH], Log[Abs[GH]] as afunction of Arg[GH], Re[θ_(tp) Q9/T_(s) ], Im[θ_(tp) Q9/T_(s)),Re[θ_(tp) /θ_(s) ], Im[_(tp) /θ_(s) ], R_(s) and X_(s), respectively,for X_(v) =0.003125(in.)--for a power steeling system utilizing thetorque reaction valve 800. The value X_(v) =0.0031.25(in.) results inF_(t) =249.1(lbs). Curve 900a in FIG. 35A depicts GH for low frequenciesto approximately 6.3(Hz) while curve 900b depicts GH for highfrequencies greater than approximately 6.3(Hz). Similarly, curve 902a inFIG. 35B depicts GH for low frequencies to approximately 6.3(Hz) whilecurve 902b depicts GH for high frequencies greater than approximately6.3(Hz).

Curve 904 in FIG. 35C depicts Re[θ_(tp) Q9/T_(s) ] while curve 906 inFIG. 35D depicts Im[θ_(tp) Q₉ /T_(s) ]. They depict a nominallycritically damped resonance at about 0.6(Hz). Curves 908 and 910depicting Re[θ_(tp) /θ_(s)) and Im[θ_(tp) /θ_(s) ], respectively, inFIGS. 35E and 35F, respectively,--as well as the curves 904 and906--depict a faster reduction in response with respect to frequencythan the curves 888, 890, 884 and 886, respectively. This is because atire patch has a lower value of torsional stiffness and a higher dampingcoefficient at higher steering load.

R_(s) and X_(s) are plotted in FIGS. 35G and 35H, respectively, ascurves 912 and 914, respectively. These curves comprise a tactile feelthat is also quite acceptable. This contrasts strongly with standardU.S. manufactured rotary valve equipped power steering systems whichshow negative values of R_(s) sat about 3(Hz). This is a highlyundesirable situation where a driver feels no steering resistance at alland is the explanation for a tactilely unstable condition at highsteering loads such as those encountered while rounding a long freewayon-ramp (with such power steering systems). Shown in FIGS. 36A-H areplots depicting Log[Abs[GH], Log[Abs[GH]] as a function of Arg[GH],Re[θ_(tp) Q9/T_(s) ], IM[θ_(tp) Q9/T_(s) ], Re[θ_(tp) /θ_(s) ],Im[θ_(tp) /θ_(s) ], R_(s) and X_(s), respectively, for X_(v) =0.001(in.)--for a power steering system which uses the torque reaction valve816. The selected value X_(v) =0.001 (in.) results in F_(t) =29.4(lbs).Curve 920a in FIG. 36A depicts GH for low frequencies to approximately5.5(Hz) while curve 920b depicts GH for high frequencies greater thanapproximately 5.5(Hz). The curve is discontinuous because of a sharpresonance in the term (myq4-(kr rw) 2/myq3+r a 2 s/myq10). Similarly,curve 922a in FIG. 36B depicts GH for low frequencies to approximately5.5(Hz) while curve 922b depicts GH for high frequencies greater thanapproximately 5.5(Hz). This curve is also discontinuous because of thesharp resonance in the term (myq4-(kr rw) 2/myq3+r a 2 s/myq10).

Curve 924 in FIG. 36C depicts Re[θ_(tp) Q9/T_(s) ] while curve 926 inFIG. 36D depicts Im[θ_(tp) Q9/T_(s) ]. They clearly depict a nominallycritically damped resonance at approximately 1(Hz). The reason for thatcan be seen in curves 920a and 922a whereat Log[Abs[GH]] equals zero. Atthat value (where Log[w] has a value of about 0.95) Abs[GH)=1.0 and hasa phase angle of about +85(deg.)--or a value that is very close to(-1)⁰.5. Thus, even though the curve 922a is to the fight of the origin,conditions depicted in the curves 924 and 926 are present.

Curves 928 and 930 depicting Re[θ_(tp) /θ_(s) ] and Im[θ_(tp) /θ_(s) ],respectively, in FIGS. 36E and 36F, respectively, are near ideal. Thus,a power steering system equipped with the torque reaction valve 816 willalso be accurately positioned but present a tactile torque lag at lowfrequency. Real and imaginary parts R_(s) and X_(s), respectively, ofthe steering wheel impedance Z_(s) =T_(s) /θ_(s) are plotted in FIGS.36G and 36H, respectively, as curves 932 and 934, respectively. Thesecurves also comprise a tactile feel that is similarly quite acceptable.

Shown in FIGS. 37A-H are plots depicting Log[Abs[GH], Log[Abs[GH]] as afunction of Arg[GH], Re[θtpQ9T_(s) ], Im[θ_(tp) Q9T_(s) ], Re[θ_(tp)/θ_(s) ], Im[θ_(tp) /θ_(s) ], R_(s) and X_(s), respectively, for X_(v)=0.00275(in.) which results in F_(t) =263.3(lbs). Curve 940a in FIG. 37Adepicts GH for low frequencies to approximately 6.1 (Hz) while curve940b depicts GH for high frequencies greater than approximately 6.1(Hz). And, curve 942a in FIG. 37B depicts GH for low frequencies toapproximately 6.1 (Hz) while curve 942b depicts GH for high frequenciesgreater than approximately 6.1 (Hz).

Curve 944 in FIG. 37C depicts Re[q_(tp) Q9/T_(s)) while curve 946 inFIG. 37D depicts Im[q_(tp) Q9/T_(s) ]. They similarly depict a nominallycritically damped resonance at about 0.7(Hz). Curves 948 and 950depicting Re[q_(tp) /q_(s) ] and Im[q_(tp) /q_(s) s], respectively, inFIGS. 37E and 37F, respectively, as well as the curves 904 and 906depict a reduction in response with respect to frequency. R_(s) andX_(s) are plotted in FIGS. 37G and 37H, respectively, as curves 952 and954, respectively. These curves also comprise a tactile feel that isquite acceptable.

Other preferred embodiments of the present invention will now bedescribed with reference to FIGS. 38-47.

Shown in FIG. 38 is a longitudinal section view (whose top and bottomhalves are taken along selected sections as described below) of avariable ratio reaction valve 1 000 which is both functionally andphysically related to the torque reaction valve 816 shown in FIG. 29.All parts thereof not specifically described below are both functionallyand physically similar to with corresponding parts of the torquereaction valve 816. Differences therebetween comprise the following:

A torsion bar 1002 having feedback torsion bar and torsion bar portions1002a and 1002b, respectively, is functionally similar to the torsionbar 817. However, it has been found that rotational indexing (duringassembly) of the feedback torsion bar 1002a with respect to a pinionshaft 1004 and the torsion bar 1002b with respect to an input shaft1006, respectively, can most easily be accomplished if the ends of thetorsion bar 1002 protrudes from the pinion shaft 1004 and the inputshaft 1006, respectively, during the indexing operation. Holes aredrilled near either end and pins 1008a and 1008b, respectively, arepressed therein. Then the ends of the torsion bar 1002 are cut off to aflush condition as indicated at 1010a and 1001b, respectively. Hydraulicfluid leakage is precluded in a known manner at each end by O-ring seals1012a and 1012b, respectively, and bushings 1014a and 1014b,respectively.

This method of assembly has an added advantage. It results in addedlength between either of the pins 1008a and 1008b and a drive pin 1016which is utilized to apply a selected portion of the input torque to aninner valve member 1018. All three pins are assembled in a substantiallyco-planer manner, as shown in FIG. 38. Thus, the torsion bar 1002 can beregarded as a beam with pinned ends in its orthogonal direction. Reduceddiameter sections 1020a and 1020b (which determine torsional springconstants of the feedback torsion bar 1002a and the torsion bar 1002b,respectively) are positioned closest to the drive pin 1016. This resultsin the torsion bar 1002 having maximum lateral compliance. Any lateralmisalignment therebetween results in minimal transverse loading of theinner valve member 1018 on an external circumferential rib 1022 formedon the input shaft 1006 and utilized as a bearing surface. Arepresentative spring rate at the drive pin 1016 is 500(lbs./in.). Thus,lateral misalignment in the order of 0.002(in.) results in a bearingloading of perhaps 1 (lb.), (No lateral misalignment occurs in the otherdirection because the drive pin is sized to be a slip fit in a centerhole 1024 of the torsion bar 1002.)

An outer valve member 1026 and a hole 1029 formed therein are positionedin line with a cylindrical cavity 1027 formed in and a pin 1030 andprotruding into, respectively, a valve sleeve 1028. Then the outer valvemember 1026 is pressed into the cavity 1027. The valve sleeve 1026 issupported by two external circumferential ribs 1032 which are formed onthe input shaft 1006 and utilized as bearing surfaces for relativerotation therebetween. Increased axial separation (with respect to anequivalent assembly of the torque reaction valve 816) between the twoexternal circumferential ribs 1032 results by positioning an input slipring 1034 outboard of output slip rings 1036. Fluid is then conductedfrom and/or to output slots 1038 via axially and radially formed holes1040a and 1040b, respectively. As in the torque reaction valve 816,pressurized fluid flows into input slots 1042 via radially formed holes1044 while return fluid flows from return slots 1046 via holes 1048formed in a barrier ring 1049. As before, the barrier ring 1049 isretained by a beveled retaining ring 1050.

However, the fundamental difference between the variable ratio reactionvalve 1000 and the torque reaction valve 816 concerns reconfigured fluidflow channels in the hydraulic interface between the inner and outervalve members 1018 and 1026, respectively. The reconfigured fluid flowchannels are shown in considerable detail in FIG. 39. Shown in FIG. 39is an enlarged section depicting a generally pie shaped segment 1051 ofthe inner and outer valve members 1018 and 1026, respectively. In FIG.39 the inner valve member 1018 is depicted in a centered position withrespect to the outer valve member 1026 as would generally be consistentwith a zero value of input torque. Also shown are portions of thetorsion bar 1002, the input shaft 1006 and the drive pin 1016.

Pressurized fluid flows through the hole 1044 to the input slot 1042 andthrough a secondary input orifice 1052 to an intermediate input chamber1054. The fluid next flows through a primary input orifice 1056 to theoutput slot 1038--from or to whence some of the fluid may flow throughthe axially formed hole 1040a. The remaining fluid then flows through asecondary return orifice 1058 to an intermediate return chamber 1060.Finally, the remaining fluid flows through a primary return orifice 1062to the return slot 1046 and out the hole 1048 (which is shown in phantombecause it is actually formed in the barrier ring 1049 which is out ofthe plane of the page).

Thus, incoming fluid is subject to additive pressure drops resultingfrom a series arrangement of the secondary and primary input orifices1052 and 1056, respectively, and returning fluid is subject to additivepressure drops resulting from a series arrangement of the secondary andprimary return orifices 1058 and 1062, respectively. The effective areacorresponding to the primary input and return orifices 1056 and 1062,respectively, is nominally similar to the effective valve area of thetorque reaction valve 816. On the other hand, the effective areacorresponding to the secondary input and return orifices 1052 and 1058,respectively, is perhaps an order of magnitude smaller.

The secondary input and return orifices 1052 and 1058, respectively, areformed in substantially the same manner as the gaps 304 and 306 in FIG.2B, and 324 and 326 in FIG. 2C, respectively, and function insubstantially the same manner. The primary input and return orifices 156and 162 are formed similarly to the input control orifices 220 and 222,and return control orifices 232 and 234, respectively. However, theprimary input and return orifices 156 and 162 are formed withsignificant radial clearance between surfaces 1064 and 1066, and 1068and 1070, respectively. Thus, they progressively cease to function ascontrol orifices concomitant with their closure as will be described inmore detail below with reference to FIGS. 40A, 40B, 41A and 41B.

The segment 1051 is depicted as a 45(deg.) segment bounded by lines1053a and 1055a. The segment 1051 is one of four substantially identicalsegments 1051 located at 90(deg.). The additional three segments 1051are bounded, in clockwise order, by lines 1057a and 1059a, 1053b and1055b, and 1057b and 1059b. Their combined outputs are hydraulicallycoupled together via one of the output slip rings 1036. In addition,there are four 45(deg.) segments 1061 which are mirror image segments tothe four segments 1051 and are bounded, in clockwise order, by lines1055a and 1057a, 1059a and 1053b, 1055b and 1057b, and 1059b and 1053a.Their combined outputs are hydraulically coupled together via the otherone of the output slip rings 1036. Because the four segments 1061 aremirror image segments to the four segments 1051, their combined outputis counter to the combined output of the four segments 1051 (i.e., whenthe output slots 1038 of the four segments 1051 are more nearly coupledto the input slots 1042, the corresponding output slots (not shown) ofthe four segments 1061 are more nearly coupled to the return slots 1046,etc.).

The drive pin 1016 and the inner valve member 1018 comprise a tooth 1072and a space 1074, respectively, on each end and proximate to each end,respectively, of the drive pin 1016 which conform generally to a singletooth and space, respectively, as listed in the specification for anAmerican Standard Involute Spline. Thus, the combined lines 1055a-1055band 1059a-1059b comprise mirror image planes of all of the partsillustrated in FIG. 39 (except for the hole 1029) while the combinedlines 1053a-1053b and 1057a-1057b comprise mirror image planes of thehydraulic interface between the inner and outer valve members 1018 and1026, respectively.

This is illustrated in a clearer manner in FIGS. 40A and 40B whichdepict the output slots 1038 of the four segments 1051 more nearlycoupled to the input slots 1042 in FIG. 40A and to the return slots 1046in FIG. 40B. The mirror image nature of the hydraulic interface betweenthe inner and outer valve members 1018 and 1026, respectively, asdescribed above can be clearly seen. In addition, FIG. 40A depicts theradial clearance present at the primary return orifice 1062 when thesecondary return orifice 1058 closes and FIG. 40B depicts the radialclearance at the primary input orifice 1056 when the secondary inputorifice 1052 closes.

This can be seen more clearly in FIGS. 41A and 41B where the primaryreturn orifice 1062 and the secondary return orifice 1058 are shown ineven greater magnification in centered and nearly closed positions,respectively. It can be seen that their respective opening dimensions vand u, respectively, are substantially the same in FIG. 41A while thedimension v is much larger than the dimension u in FIG. 41 B. Becausepressure drop at each orifice is nominally proportional to its areasquared, the pressure drop at the secondary orifice 1058 (i.e.,indicated by the smaller dimension "u") becomes progressively dominantas valve closure occurs. Therefore, because the radial distance betweenthe secondary orifices 1052 and 1058 is much smaller than the radialdistance between the primary orifices 1056 and 1062, the effectivereaction area of the variable reaction valve 1000 also becomesprogressively smaller as valve closure occurs.

Thus, modifying the static response characteristic of a reaction valvesuch that its gain decreases as a function of output pressure can beaccomplished via the method of utilizing multiple orifices withdiffering closure characteristics and placing them hydraulically inseries therein. The multiple orifices utilized in implementing thismethod comprise sets of orifices which control pressures present inreaction zones having differing effective areas. And, the closurecharacteristic of the set, or sets, of orifices which control pressuresin the reaction zones having the largest effective areas comprises anincomplete closure characteristic relative to the closure characteristicof the set, or sets, of orifices which control pressures in the reactionzones having smaller effective areas.

One method of forming the inner and outer members 1018 and 1026,respectively, is by a metal removal process known as broaching.Broaching involves progressively cutting a desired contour in a part viasequential removal of material with a progression of culling teeth on alongitudinal tooling member known as a broach. Generally this can bethought of as a progressive process whereby the part in questionprogressively approximates its final appearance as the cutting teethpass by, or through the part. However, because it is desirable to formvarious adjacent surfaces where between corners which define the primaryand secondary orifices 1056 and 1062, and 1052 and 1058, respectively,such that these corners are nominally sharp corners, broaching of thesetwo parts should be thought of as two distinct operations.

This is illustrated by FIGS. 42 and 43 which depict first and secondbroaching operations utilized in forming the hydraulic interfacesurfaces on the inner valve member 1018 and the outer valve member 1026,respectively. The first broaching operation serves to configure theinner valve member in an intermediate manner as indicated by the outerline 1076 in FIG. 42 and the inner line 1078 in FIG. 43. The secondbroaching operation serves to reconfigure the inner and outer valvemembers 1018 and 1026 in final form by removing the material indicatedby cross-hatched areas 1080 and 1081, and 1082 and 1083 in FIGS. 42 and43, respectively. The spline spaces 1074 and the hole 1029 can beutilized for indexing the inner and outer valve members 1018 and 1026,respectively, during the first and second broaching operations.Alternately, either of the parts can be formed by first and secondbroaching operations performed concomitantly by two sequential sets ofcutting teeth on a single broach.

In operation, the input shaft 1006, the inner valve member 1018 and anassembly comprising the outer valve member 1026, the valve sleeve 1028and the barrier ring 1049 must be free to rotate relative to oneanother. As described above, the circumferential rib 1022 and ribs 1032support the inner valve member 1018 and the valve sleeve 1028,respectively, for rotation with respect to the input shaft 1006. Theinner valve member 1018 is guided axially and in pitch and yaw withinthe outer valve member 1026 by a shoulder 1084, formed as a definingwall of the cavity 1027 of the valve sleeve 1028, and the barrier ring1049. The axial spacing between the shoulder 1084 and the barrier ring1049 is determined by the axial length of the outer valve member 1026.Thus, the axial clearance between the inner valve member 1018 and eitherof the shoulder 1084 and the barrier ring 1049 is nominally one-half ofthe difference between the axial thicknesses of the outer valve member1026 and the inner valve member 1018.

In order to maintain rotational freedom for the inner valve member, itis desirable to avoid the condition known as "hydraulic lock" describedhereinabove. Hydraulic lock is discussed in considerable depth in asection 5-7 entitled LATERAL FORCES ON SPOOL VALVES of the book entitledHYDRAULIC CONTROL SYSTEMS for the case of spool valves. One passagetherein reads as follows:

"If the higher pressure is at the small end of the piston the lateralforce acts to center the piston. If there is a distinct high pressureside on the piston, an intentional taper to that side could be used toobtain a centering force to prevent hydraulic lock. However, this is notpractical, especially on spool valves, because the taper direction wouldbe different on the various valve lands, making manufacture mostdifficult."

However, contrary to the above statement, the inner valve member 1018has a "distinct pressure side" in the form of the outer peripherythereof. Thus, in one preferred embodiment, a generally convex conicalor spherical "taper" formed on each side of the inner valve member 1018can be used to obtain an equivalent centering force to the one calledfor above. In fact, the resulting inwardly radial flow passages compriseopposing hydrostatic bearings. This is depicted descriptively in FIG.44A by inward radial flow passages 1085a and 1085b (whose curvature isgreatly distorted to illustrate the concept). One method of formingspherically convex surfaces on the inner valve member 1018 is by lappingthem to a very large radius. Such technology is readily available withinthe optics industry and is easily adaptable for this purpose. Typicaldimensions comprise an overall axial clearance dimension between theinner valve member 1018 and the space between the shoulder 1084 and thebarrier ring 1049 of perhaps 0.0003(in.) and spherical surface radii ofperhaps 30 inches.

In another preferred embodiment, alternate hydrostatic bearing flowpassages 1086a and 1086b can be formed via stepped surfaces 1087a and1087b, respectively, which are formed on the shoulder 1084 and thebarrier ring 1049, respectively, as depicted in FIG. 44B. In this caseit is also convenient to fabricate both the inner and outer valvemembers 1018 and 1026, respectively, at precisely the same thickness(i.e., as with parallel laps). Overall axial clearance is provided byadditional spacing shoulders 1088a and 1088b formed on the shoulder 1084and the barrier ring 1049, respectively. Typical dimensions comprise theabove noted overall axial clearance of 0.0003(in.) combined with steppedsurface heights of 0.0001 (in.).

It is important not to over-constrain the inner valve member viaconstricting an interface with the circumferential rib 1022. Thus, thecircumferential rib 1022 is narrower than the inner valve member 1018(forming it as an equatorial segment of a sphere would even be better.The requirement for such non-constraint is indicated by a radial gap1088 between the input shaft 1006 and the inner valve member 1018 inFIG. 39.)

In addition, it is also important not to drive the inner valve member1018 asymmetrically by the drive pin 1016 via the mechanical interfacecomprising the teeth 1072 and the spaces 1074. This possibility can beprecluded by forming the teeth 1072 in a crowned manner as shown in FIG.45. One method of so fabricating the teeth 1072 is to rotate the drivepin 1016 about axis 1090 (i.e., an axis in and out of the plane of thepage) in a cylindrical grinder and plunge grind the contours comprisedin the teeth 1072.

Detailed analysis and plotting of the functions utilized hereinbefore isperformed generally as shown above. However, slight changes in theprograms are required to accommodate the new primary and secondaryorifices. A revised first program utilized for typical plots of steeringforce as functions of applied torque, tangential valve motion and inputshaft rotation is as follows:

    ______________________________________                                        kt = 1080.0;                                                                  kf = 1080.0;                                                                  lve = 1.0;                                                                    rv1 = 0.585;                                                                  av1 = 0.1;                                                                    rv2 = 0.585;                                                                  av2 = 0.005;                                                                  xo1 = 0.008;                                                                  xo2 = xo1 rv2/rv1;                                                            xv1[xv.sub.-- ]:= xv;                                                         xv2[xv.sub.-- ]:= xv1[xv] rv2/rv1;                                            gap = 0.002;                                                                  qs = 6;                                                                       lp = 0.0001;                                                                  r = 100;                                                                      tv1[xv.sub.-- ]:= rv1 av1 qs 2/(90000 lve 2 ((xo1 - xv1[xv]) 2 + gap          2));                                                                          tv2[xv.sub.-- ]:= rv2 av2 qs 2/(90000 lve 2 (xo2 - xv2[xv]) 2);               tv[xv.sub.-- := tv1[xv] + tv2[xv];                                            ts[xv.sub.-- := tv[xv] + kf xv1[xv]/rv1;                                      kv1[xv.sub.-- ]:= rv1 av1 qs 2 (xo1 - xv1[xv])/(45000 lve 2 ((xo1 -           xv1[xv]) 2 +                                                                  gap 2));                                                                      kv2[xv.sub.-- ]:= rv2 av2 qs 2/(45000 lve 2 (xo2 - xv2[xv]) 3);               kv[xv] := kv1[xv] + kv2[xv];                                                  k2[xv.sub.-- ]:= kt kv[xv]/(kt (kv[xv] + kf));                                np = 0.333333;                                                                fm[xv.sub.-- ]:= ts[xv]/np;                                                   a = 1.0;                                                                      fp[xv.sub.-- ]:= tv1[xv] a/(rv1 av1 (1 + rlp)) + tv2[xv] a/(rv2 av2 (1 +      rlp));                                                                        ft[xv.sub.-- ]:= fm[xv] + fp[xv];                                             thetae[xv.sub.-- ]:= ts[xv]/kt;                                               thetav[xv.sub.-- ]:= xv1[xv]/rv1;                                             thetas[xv.sub.-- ]:= thetae[xv] + thetav[xv];                                 ______________________________________                                    

where "gap" is the radial clearance present at both the primary inputand return orifices 1056 and 1062, respectively, when they are closed.(Note, if it was desired to have different "gaps" for the primary inputand return orifices 1056 and 1062, respectively--or a modified hydraulicinterface between the inner valve member 1018 and the outer valve member1026 such that the "gaps" varied as a function of relative position ofthe inner valve member 1018--further program modification of both thefirst and second programs would be necessary. i.e., see furtherdiscussion below for a description of modifications which can beutilized to achieve such variable "gaps".)

Shown in FIGS. 46A-C are curves 1092a-c, respectively which depict theoutput force F_(t) as a function of T_(S), X_(v) and θ_(s),respectively, via utilization of the above values for one example of thevariable ratio reaction valve 1000. A revised second program utilizedfor typical plots of system performance is as follows:

    ______________________________________                                        xv = 0.0065;                                                                  js = 0.32;                                                                    bs = 0.0;                                                                     ksc = 3200.0;                                                                 kt = 1080.0;                                                                  kf = 1080.0;                                                                  lve = 1.0;                                                                    rv1 = 0.585;                                                                  av1 = 0.1;                                                                    rv2 = 0.585;                                                                  av2 = 0.005;                                                                  xo1 = 0.008;                                                                  xo2 = xo1 rv2/rv1;                                                            xv1 = xv;                                                                     xv2 = xv rv2/rv1;                                                             gap = 0.002;                                                                  qs = 6;                                                                       lp = 0.0001;                                                                  r = 100;                                                                      pv1 = qs 2/(90000 lve 2 ((xo1 - xv1) 2 + gap 2));                             pv2 = qs 2/(90000 lve 2 (xo2 - xv2) 2);                                       tv1 = rv1 av1 pv1;                                                            tv2 = rv2 av2 pv2;                                                            tv = tv1 + tv2;                                                               ts = tv + kf xv1/rv1;                                                         tf = ts - tv;                                                                 kv1 = rv1 av1 qs 2 (xo1 - xv1)/(45000 lve 2 ((xo1 - xv1) 2 + gap 2));         kv2 = rv2 av2 qs 2/(45000 lve 2 (xo2 - xv2) 3);                               kv = kv1 + kv2;                                                               k1 = kt (kv + kf)/(kt + kv + kf);                                             k4 = ksc/(ksc + k1)                                                           k2 = kt kv/(kt (kv + kf));                                                    np = 0.333333;                                                                fm = ts/np;                                                                   a = 1.0;                                                                      fp = tv1 a/(rv1 av1 (1 + rlp)) + tv2 a/(rv2 av2 (1 + rlp));                   ft = fm + fp;                                                                 xp = -Log[1 - ft/400]/1.5;                                                    ktp = 15000.0 E (-1.5 xp);                                                    btp = 250 + 500 xp + 87.5 xp 2;                                               ksw = 25000.0;                                                                bsw = 100.0;                                                                  jw = 6.25;                                                                    rw = 5.0;                                                                     kr = 4000.0;                                                                  mp = 0.025;                                                                   bp = 2.0;                                                                     q1[s.sub.-- ]:= bsw s + ksw;                                                  q2[s.sub.-- ]:= (btp + bsw) s + ktp + ksw;                                    q3[s.sub.-- ]:= jw s 2 + q1[s] - q1[s] 2/q2[s] + kr rw 2;                     q4[s.sub.-- ]:= mp s 2 + bp s + kr;                                           tau = 0.005;                                                                  kc = 0.000025;                                                                pi = N[ Pi, 10];                                                              q5[s.sub.-- ]:= tau s + 1;                                                    q8[s.sub.-- ]:= js s 2 + bs s + k1 k4;                                        q9[s.sub.-- ]:= js s 2 + bs s;                                                q10[s.sub.-- ]:= 1 + r (kc s + lp);                                           go[s.sub.-- ]:= Block[{myq3,myq4,myq5,myq10},                                 myq3 = q3[s];                                                                 myq4 = q4[s];                                                                 myq5 = q5[s];                                                                 myq10 = q10[s];                                                               N[k4 (k1/np + k1 k2 (pv1 + pv2) a/ (myq5 myq10 tv))/                           (myq4 - (kr rw) 2/myq3 + r a 2 s/myq10),                                      10]];                                                                        ho = N[1/np , 10];                                                            g[s.sub.-- ]:= Block[{myq3,myq4,myq5,myq8,myq10},                             myq3 = q3[s];                                                                 myq4 = q4[s];                                                                 myq5 = q5[s];                                                                 myq8 = q8[s];                                                                 myq10 = q10[s];                                                               N[k4 (k1/np + k1 k2 (pv1 + pv2) a/ (myq5 myq10 tv))/                           (myq8 (myq4 - (kr rw) 2/myq3 + r a 2 s/myq10)), 10]];                        h[s.sub.-- ]:= N[q9[s]/np , 10];                                              ______________________________________                                    

Shown in FIGS. 47A-H are plots depicting Log[Abs[GH], Log[Abs[GH]]as afunction of Arg[GH], Re[θ_(tp) Q9/T_(s) ], Im[θ_(tp) Q9/T_(s) ],Re[θ_(tp) /θ_(s) ], Im[θ_(tp) /θ_(s) ], R_(s) and X_(s), respectively,for a power steering system which uses the variable ratio reaction valve1000 at a steering load of approximately 290(lbs.). As before, thesecurves depict a tactile feel that is quite acceptable.

It is possible to modify the closure characteristic of either, or both,of the primary input and return orifices 1056 and 1062 and thus modifythe static response characteristic of a modified variable ratio reactionvalve 1000a, and still be within the scope of the present invention. Forinstance, if the closure characteristics of either, or both, of theprimary input and return orifices 1056 and 1062 are modified to formmodified primary input and return orifices 1056a and 1062a,respectively, so that closure thereof occurs at a slower rate than thatof the secondary input and return orifices 1052 and 1058, respectively,then dominant pressure control smoothly inverts from the primary sets ofcontrol orifices to the secondary sets of control orifices, (i.e., atthe centered position the dimension v is smaller than dimension u, butfinally the dimension u becomes smaller than the dimension v as thevalve closes.) Thus, the affective reaction area will be larger wheneversuch a version of the variable ratio reaction valve is substantiallyopen and an even wider range of output pressure to input torque gain isenabled.

This can be accomplished as depicted in FIGS. 48A-B and 49A-B whereinsuch modified primary input and return orifices 1056a and 1062a,respectively, are shown in centered and substantially closed positions(i.e., in manner equivalent to the depiction in FIGS. 41A and 41B). Inaddition to the dimensions u and v which are carried over from FIGS. 41Aand 41B, dimensions w and y are used in FIGS. 48A and 48B for theprimary and secondary input orifices 1052 and 1056a, respectively. InFIGS. 48A and 49A the dimensions y and v are indeed smaller than thedimensions w and u, respectively, while in FIGS. 48B and 49B thedimensions w and u are smaller than the dimensions y and v,respectively. This is because surfaces 1094 and 1096, which partiallydefine the modified primary input and return orifices 1056a and 1062a,respectively, are now formed at angles αand β, respectively, with acircumferential direction. If surfaces 1098 and 1100, which partiallydefine the secondary input and return orifices 1052 and 1058,respectively, are formed at angles φ and γ, respectively, with a radialdirection then the dimensions u, v, w and y can be evaluated by

u=(x_(o) -X) cosγ,

v=(x₁ -x) sinβ,

w=(x_(o) -x) cosφ and

y=(x₁ -x) sinα

where x_(o) is the tangential distance the modified variable ratioreaction valve 1000a can move from a centered position to completelyclosed position, x₁ is the tangential clearance at either of themodified primary input and return orifices 1056a and 1062a (which is, ingeneral, larger than x_(o)) and x is a tangential distance actuallymoved by the modified variable ratio reaction valve toward closurethereof.

It can be seen that if all of the angles α, β, φ and γ are smaller than45(deg.) then the above criterion can be satisfied. For instance, ifx_(o) =0.009(in.),x₁ =0.011(in.),α=β=30(deg.) and φ=γ=15(deg.), theu=w=0.0087(in.) and v=y=0.0055(in.) at x=0.0(in.)-and u=w=0.0010(in.)and v=y=0.0015(in.) at x=0.0080(in.). Thus, the modified hydraulicinterface between the inner valve member 1018 and the outer valve member1026 having "gaps" which vary as a function of relative position of theinner valve member 1018 called for above can indeed be achieved. Inaddition, the second broaching operation can be simplified to the extentthat the cross-hatched areas 1081 and 1083 need not be present andtherefore no longer require removal thereby. This is shown in FIGS. 50and 51 which are enlarged end views of a modified inner valve member1018a and a modified outer valve member 1026a, respectively, of themodified variable ratio reaction valve 1000a.

Thus, the method of modifying the static response characteristic of areaction valve such that its gain decreases as a function of outputpressure can be extended via altering the nature of the orifice closuresas described above. In this case the method comprises smoothly invertingdominant pressure control from primary to secondary sets of controlorifices which are in series arrangement, thereby extending the range ofeffective reaction zone areas even further.

As noted above, further program modification of both the first andsecond programs is necessary in order to depict the performance of themodified variable ratio reaction valve 1000a. The respective modifiedfirst and second programs are as follows:

    ______________________________________                                        kt = 1080.0;                                                                  kf = 360.0;                                                                   lve = 1.0;                                                                    rv1 = 0.585;                                                                  av1 = 0.1;                                                                    rv2 = 0.585;                                                                  av2 = 0.01;                                                                   xo1 = 0.009;                                                                  xo2 = xo1 rv2/rv1;                                                            x11 = 0.011;                                                                  x12 = x11 rv2/rv1;                                                            xv1[xv.sub.-- ]:= xv;                                                         xv2[xv.sub.-- ]:= xv1[xv] rv2/rv1;                                            beta = 0.524;                                                                 gamma = 0.262;                                                                qs = 6;                                                                       lp = 0.0001;                                                                  r = 100;                                                                      gap1 = x11 Sin[beta];                                                         gap2 = (x11 - xo2 + 0.001) Sin[beta];                                         tv1[xv.sub.-- ]:= rv1 av1 qs 2/(90000 lve 2 (x11 - xv1[xv]) 2 Sin[beta]       2);                                                                           tv2[xv.sub.-- ]:= rv2 av2 qs 2/(90000 lve 2 (xo2 - xv2[xv]) 2 Cos[gamma]      2);                                                                           tv[xv.sub.-- ]:= tv1[xv] + tv2[xv];                                           ts[xv.sub.-- ]:= tv[xv] + kf xv1[xv]/rv1;                                     kv1[xv.sub.-- ]:= rv1 av1 qs 2/(45000 lve 2 (xo1 - xv1[xv]) 3 Sin[beta]       2);                                                                           kv2[xv.sub.-- ]:= rv2 av2 qs 2/(45000 lve 2 (xo2 - xv2[xv]) 3 Cos[gamma]      2);                                                                           kv[xv.sub.-- ]:= kv1[xv] + kv2[xv];                                           k2[xv.sub.-- ]:= kt kv[xv]/(kt (kv[xv] + kf));                                np = 0.333333;                                                                fm[xv.sub.-- ]:= ts[xv]/np;                                                   a = 1.0;                                                                      fp[xv.sub.-- ]:= tv1[xv] a/(rv1 av1 (1 + rlp)) + tv2[xv] a/(rv2 av2 (1 +      rlp));                                                                        ft[xv.sub.-- ]:= fm[xv] + fp[xv];                                             thetae[xv.sub.-- ]:= ts[xv]/kt;                                               thetav[xv.sub.-- ]:= xv1[xv]/rv1;                                             thetas[xv.sub.-- ]:= thetae[xv] + thetav[xv];                                 and                                                                           xv = 0.0075;                                                                  js = 0.32;                                                                    bs = 0.0;                                                                     ksc = 3200.0;                                                                 kt = 1080.0;                                                                  kf = 360.0;                                                                   lve = 1.0;                                                                    rv1 = 0.585;                                                                  av1 =  0.1;                                                                   rv2 = 0.585;                                                                  av2 = 0.01;                                                                   xo1 = 0.009;                                                                  xo2 = xo1 rv2/rv1;                                                            x11 = 0.011;                                                                  x12 = x11 rv2/rv1;                                                            xv1 = xv;                                                                     xv2 = xv rv2/rv1;                                                             beta = 0.524;                                                                 gamma = 0.262;                                                                qs = 6;                                                                       lp = 0.0001;                                                                  r = 100;                                                                      gapp = (x11 - xv1) Sin[beta];                                                 gaps = (xo2 - xv2) Cos[gamma];                                                pv1 = qs 2/(90000 lve 2 (x11 - xv1) 2 Sin[beta] 2);                           pv2 = qs 2/(90000 lve 2 (xo2 - xv2) 2 Cos[gamma] 2);                          tv1 = rv1 av1 pv1;                                                            tv2 = rv2 av2 pv2;                                                            tv = tv1 + tv2;                                                               ts = tv + kf xv1/rv1;                                                         tf = ts - tv;                                                                 thetas = ts/kt + xv/rv1;                                                      kv1 = rv1 av1 qs 2/(45000 lve 2 (xo1 - xv1) 3 Sin[beta] 2);                   kv2 = rv2 av2 qs 2/(45000 lve 2 (xo2 - xv2) 3 Cos[gamma] 2);                  kv = kv1 + kv2;                                                               k1 = kt (kv + kf)/(kt + kv + kf);                                             k4 = ksc/(ksc + k1)                                                           k2 = kt kv/(kt (kv + kf));                                                    np = 0.333333;                                                                fm = ts/np;                                                                   a = 1.0;                                                                      fp = tv1 a/(rv1 av1 (1 + rlp)) + tv2 a/(rv2 av2 (1 + rlp));                   ft = fm + fp;                                                                 xp = -Log[1 - ft/400]/1.5;                                                    ktp = 15000.0 E (-1.5 xp);                                                    btp = 250 + 500 xp + 87.5 xp 2;                                               ksw = 25000.0;                                                                bsw = 100.0;                                                                  jw = 6.25;                                                                    rw = 5.0;                                                                     kr = 4000.0;                                                                  mp = 0.025;                                                                   bp = 2.0;                                                                     q1[s.sub.-- ]:= bsw s + ksw;                                                  q2[s.sub.-- ]:= (btp + bsw) s + ktp + ksw;                                    q3[s.sub.-- ]:= jw s 2 + q1[s] - q1[s] 2/q2[s] + kr rw 2;                     q4[s.sub.-- ]:= mp s 2 + bp s + kr;                                           tau = 0.005;                                                                  kc =  0.000025;                                                               pi = N[Pi, 10];                                                               q5[s.sub.-- ]:= tau s + 1;                                                    q8[s.sub.-- ]:= js s 2 + bs s + k1 k4;                                        q9[s.sub.-- ]:= js s 2 + bs s;                                                q10[s.sub.-- ]:= 1 + r (kc s + lp);                                           go[s.sub.-- ]:= Block[{myq3,myq4,myq5,myq10},                                 myq3 = q3[s];                                                                 myq4 = q4[s];                                                                 myq5 = q5[s];                                                                 myq10 = q10[s];                                                               N[k4 (k1/np + k1 k2 (pv1 + pv2) a/(myq5 myq10 tv))/                            (myq4 - (kr rw) 2/myq3 + r a 2 s/myq10),                                      10]];                                                                        ho = N[1/np , 10];                                                            g[s.sub.-- ]:= Block[{myq3,myq4,myq5,myq8,myq10},                             myq3 = q3[s];                                                                 myq4 = q4[s];                                                                 myq5 = q5[s];                                                                 myq8 = q8[s];                                                                 myq10 = q10[s];                                                               N[k4 (k1/np + k1 k2 (pv1 + pv2) a/(myq5 myq10 tv))/                            (myq8 (myq4 - (kr rw) 2/myq3 + r a 2 s/myq10)) , 10]];                       h[s.sub.-- ]:= N[q9[s]/np , 10];                                              ______________________________________                                    

The values chosen result in steering force curves which differconsiderably from those in FIGS. 46A-C. Shown in FIGS. 52A-C are plotsdepicting steering force as a function of applied torque, tangentialvalve motion and input shaft rotation, respectively, for the modifiedvariable ratio reaction valve 1000a (when these values are utilized).Although these sets of curves differ greatly, they do not representlimits of any kind. There are enough variables available for selectionthat virtually any plausible curve shapes can be obtained.

Shown in FIGS. 53A-H are plots depicting performance of a power steeringsystem utilizing these values for the modified variable ratio reactionvalve. Even though these values yield the dramatic changes in (static)steering forces, mentioned above, there is remarkably little change inany of the (dynamic) performance curves between those shown in FIGS.47A-H and 53A-H.

I claim:
 1. An apparatus for generating a hydraulic fluid pressure froman input torque, the ratio of said hydraulic fluid pressure to inputtorque being variable, said apparatus comprising:an input shaft operableto receive said input torque; a first valve member coupled to said inputshaft; a second valve member being in fluid communication with saidfirst valve member via a hydraulic interface, said second valve memberbeing coupled to a reference member, said hydraulic interface havingprimary and second sets of input and return orifices, said primary andsecondary sets of input and return orifices being selectively utilizedto define effective reaction areas as a function of said input torque,said primary and secondary sets of input and return orifices beinglocated at selected radii; said selected radii locating said primarysets of input and return orifices are first and second radii,respectively, wherein said first radii are smaller in value than saidsecond radii; said selected radii locating said secondary sets of inputand return orifices are third and fourth radii, respectively, whereinsaid third radii are smaller in value than said fourth radii; thedifference between said second radii and said first radii is greaterthan the difference between said fourth radii and said third radii;means for inducing hydraulic fluid to flow through said hydraulicinterface; and means for coupling hydraulic fluid in directcommunication with said hydraulic interface to a hydraulic load.
 2. Theapparatus of claim 1, wherein said hydraulic fluid pressure isfluidically coupled to a utilization device and said reference member ismechanically coupled to an output member of said utilization device. 3.The apparatus of claim 2, wherein said first valve member is compliantlycoupled to said input shaft.
 4. The apparatus of claim 2, furthercomprising means for compliantly coupling said first valve member tosaid reference member.
 5. The apparatus of claim 3, further comprisingmeans for compliantly coupling said first valve member to said referencemember.
 6. The apparatus of claim 1, wherein at least one of saidprimary sets of input and return orifices is defined by first and secondsets of nominally sharp edged corners wherein:said first set ofnominally sharp edged corners is comprised in said first valve member;said second set of nominally sharp edged corners is comprised in saidsecond valve member; and said first and second sets of nominally sharpedged corners are located at slightly differing first and second radii,respectively, wherein said second radii are larger than said first radiisuch that said at least one of said primary sets of orifices cannotcompletely close when any of said secondary sets of orifices arecompletely closed.
 7. The apparatus of claim 1, wherein at least one ofsaid primary sets of input and return orifices is defined by a set ofnominally sharp edged corners and a set of surfaces located at otherthan an orthogonal angle with a radial direction wherein:said set ofnominally sharp edged corners is comprised on one of said first orsecond valve members; said set of surfaces is comprised on the other ofsaid first or second valve members; and said set of nominally sharpedged corners and said set of surfaces are proximate to one another butlocated such that they do not come in contact when any of said secondarysets of orifices are completely closed.
 8. An apparatus for generatingan output force from an input torque, the ratio of said output force toinput torque being variable, said apparatus comprising:an input shaftoperable to receive said input torque; a first valve member coupled tosaid input shaft; a second valve member being in fluid communicationwith said first valve member via a hydraulic interface, said secondvalve member being coupled to an output member, said hydraulic interfacehaving primary and secondary sets of input and return orifices, saidprimary and secondary sets of input and return orifices beingselectively utilized to define effective reaction areas as a function ofsaid input torque, said primary and secondary sets of input and returnorifices being located at selected radii; said selected radii locatingsaid primary sets of input and return orifices are first and secondradii, respectively, wherein said first radii are smaller in value thansaid second radii; said selected radii locating said secondary sets ofinput and return orifices are third and fourth radii, respectively,wherein said third radii are smaller in value than said fourth radii;the difference between said second radii and said first radii is greaterthan the difference between said fourth radii and said third radii;means for inducing hydraulic fluid to flow through said hydraulicinterface; means for generating said output force in response to anapplied hydraulic fluid pressure; and means for coupling hydraulic fluidfrom said hydraulic interface to said means for generating said outputforce.
 9. The apparatus of claim 8, wherein said first valve member iscompliantly coupled to said input shaft.
 10. The apparatus of claim 8,further comprising means for compliantly coupling said first valvemember to said output member of said means for generating said outputforce.
 11. The apparatus of claim 8, further comprising means forcompliantly coupling said first valve member to said output member ofsaid means for generating said output force.
 12. The apparatus of claim8, wherein said hydraulic interface comprises primary and secondary setsof input and return orifices, said primary and secondary sets of inputand return orifices being selectively utilized to define said effectivereaction areas as a function of said input torque.
 13. The apparatus ofclaim 8, wherein at least one of said primary sets of input and returnorifices is defined by first and second sets of nominally sharp edgedcorners wherein:said first set of nominally sharp edged corners iscomprised in said first valve member; said second set of nominally sharpedged corners is comprised in said second valve member; and said firstand second sets of nominally sharp edged corners are located at slightlydiffering first and second radii, respectively, wherein said secondradii are larger than said first radii such that said at least one ofsaid primary sets of orifices cannot completely close when any of saidsecondary sets of orifices are completely closed.
 14. The apparatus ofclaim 8, wherein at least one of said primary sets of input and returnorifices is defined by a set of nominally sharp edged corners and a setof surfaces located at other than an orthogonal angle with a radialdirection wherein:said set of nominally sharp edged corners is comprisedon one of said first or second valve members; said set of surfaces iscomprised on the other of said first or second valve members; and saidset of nominally sharp edged corners and said set of surfaces areproximate to one another but located such that they do not come incontact when any of said secondary sets of orifices are completelyclosed.
 15. A method for allowing an operator of a power assistedsteering system to generate an output steering force comprising thesteps of:delivering an input torque to an input member whichmechanically communicates with a first valve member; forming a set ofprimary input and return orifices defined by first and second radiiwherein said first radii are smaller than said second radii; forming aset of secondary input and return orifices defined by third and fourthradii wherein said third radii are smaller than said fourth radii;forming said primary and secondary orifices such that the differencebetween said second radii and said first radii is greater than thedifference between said fourth radii and said third radii; generating anoutput hydraulic pressure in response to pressure developed within avariable effective reaction area comprised within a hydraulic interfacedefined by said primary and secondary sets of input and return orificesbetween said first valve member and a second valve member; andgenerating an output steering force in response to said output hydraulicpressure in which the ratio of said output steering force to said inputtorque is variable.
 16. The method of claim 15, wherein said outputhydraulic pressure is substantially inversely proportional to saidvariable effective reaction area and said variable effective reactionarea is a selected function of said input torque, said method comprisingthe additional step of generating said output steering force as a linearfunction of the ratio of said input torque divided by said variableeffective reaction area.
 17. The method of claim 16, wherein said powerassisted steering system comprises an input shaft, said methodcomprising the additional step of compliantly coupling said first valvemember to said input shaft.
 18. The method of claim 16, wherein saidpower assisted steering system comprises a power cylinder for generatingsaid output steering force in response to said output hydraulic pressureand a reference member which is coupled to an output member of saidpower cylinder, said method comprises the additional step of couplingsaid second valve member to said reference member.
 19. The method ofclaim 18, wherein said method comprises the additional step ofcompliantly coupling said first valve member to said reference member.20. The method of claim 17, wherein said power assisted steering systemcomprises a power cylinder for generating said output steering force inresponse to said output hydraulic pressure and a reference member whichis coupled to an output member of said power cylinder, said methodcomprises the additional step of coupling said second valve member tosaid reference member.
 21. The method of claim 20, wherein said methodcomprises the additional step of compliantly coupling said first valvemember to said reference member.